Gerak melingkar - Wikipedia bahasa Indonesia, ensiklopedia bebas

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.sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style> <table class="sidebar sidebar-collapse"> <tbody> <tr> <td class="sidebar-pretitle">Bagian dari seri artikel mengenai</td> </tr> <tr> <th class="sidebar-title-with-pretitle" style="padding-left:0.9em;padding-right:0.9em;"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Mekanika_klasik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Mekanika klasik">Mekanika klasik</a></th> </tr> <tr> <td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {F}}=m{\vec {a}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> F </mi> <mo stretchy="false"> → </mo> </mover> </mrow> </mrow> <mo> = </mo> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> a </mi> <mo stretchy="false"> → </mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\vec {F}}=m{\vec {a}}} </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7b202a8eaba4b424be52bcbaa043727b6ad9860" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.14ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}=m{\vec {a}}}"></span> <div class="sidebar-caption" style="font-size:90%;padding:0.6em 0;font-style:italic;"> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Hukum_kedua_Newton?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Hukum kedua Newton">Hukum kedua Newton</a> </div></td> </tr> <tr> <th class="sidebar-heading" style="background:#ddf; display:block;margin-bottom:1.0em;"> <div class="hlist" style="margin-left: 0em;"> <ul> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Sejarah_mekanika_klasik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sejarah mekanika klasik">Sejarah</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Garis_waktu_mekanika_klasik&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Garis waktu mekanika klasik (halaman belum tersedia)">Garis waktu</a></li> </ul> </div></th> </tr> <tr> <td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"> <div class="sidebar-list-title" style="background:#ddf;text-align:center;"> Cabang </div> <div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"> <div class="hlist" style="margin-left: 0em;"> <ul> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Mekanika_benda_langit?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Mekanika benda langit">Benda langit</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Analisa_dinamika&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Analisa dinamika (halaman belum tersedia)">Dinamika</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Kinematika?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kinematika">Kinematika</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Kinetika_(fisika)&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Kinetika (fisika) (halaman belum tersedia)">Kinetika</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Mekanika_kontinuum?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Mekanika kontinuum">Kontinuum</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Statika?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Statika">Statika</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Mekanika_statistika?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Mekanika statistika">Statistika</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Mekanika_terapan?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Mekanika terapan">Terapan</a></li> </ul> </div> </div> </div></td> </tr> <tr> <td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"> <div class="sidebar-list-title" style="background:#ddf;text-align:center;"> Dasar </div> <div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"> <div class="hlist" style="margin-left: 0em;"> <ul> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D%27Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Asas D'Alembert">Asas D'Alembert</a></li> <li><br><a href="https://id-m-wikipedia-org.translate.goog/wiki/Daya?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Daya">Daya mekanik</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Energi?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Energi">Energi</a> <ul> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Energi_kinetik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Newtonian_kinetic_energy" title="Energi kinetik">kinetik</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Energi_potensial?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Energi potensial">potensial</a></li> </ul></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gaya_(fisika)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gaya (fisika)">Gaya</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Impuls_(fisika)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Impuls (fisika)">Impuls</a></li> <li><span class="nowrap"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Inersia?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Inersia">Inersia</a> / <a href="https://id-m-wikipedia-org.translate.goog/wiki/Momen_inersia?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Momen inersia">Momen inersia</a></span></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Kecepatan?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kecepatan">Kecepatan</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Kelajuan?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kelajuan">Kelajuan</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Kerangka_acuan?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kerangka acuan">Kerangka acuan</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Usaha_(fisika)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Usaha (fisika)">Usaha mekanik</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Kerja_maya?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kerja maya">Kerja maya</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Massa?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Massa">Massa</a></li> <li><br><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Momen_(fisika)&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Momen (fisika) (halaman belum tersedia)">Momen</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Momentum?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Momentum">Momentum</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Momentum_sudut?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Momentum sudut">Momentum sudut</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Pasangan_(mekanika)&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Pasangan (mekanika) (halaman belum tersedia)">Pasangan</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Percepatan?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Percepatan">Percepatan</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Ruang?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Ruang">Ruang</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Torsi?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Torsi">Torsi</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Waktu?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Waktu">Waktu</a></li> </ul> </div> </div> </div></td> </tr> <tr> <td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"> <div class="sidebar-list-title" style="background:#ddf;text-align:center;"> Rumus </div> <div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"> <ul> <li> <div style="display:inline-block; padding:0.1em 0;line-height:1.2em;"> <b><a href="https://id-m-wikipedia-org.translate.goog/wiki/Hukum_gerak_Newton?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Hukum gerak Newton">Hukum gerak Newton</a></b> </div></li> <li> <div style="display:inline-block; padding:0.1em 0;line-height:1.2em;"> <b><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Mekanika_analisis&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Mekanika analisis (halaman belum tersedia)">Mekanika analisis</a></b><br> <div style="display:inline-block; padding:0.1em 0;line-height:1.2em;"> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Mekanika_Lagrangian?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Mekanika Lagrangian">Mekanika Lagrange</a><br><a href="https://id-m-wikipedia-org.translate.goog/wiki/Mekanika_Hamiltonian?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Mekanika Hamiltonian">Mekanika Hamilton</a><br><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Mekanika_Routh&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Mekanika Routh (halaman belum tersedia)">Mekanika Routh</a><br><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Persamaan_Hamilton%E2%80%93Jacobi&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Persamaan Hamilton–Jacobi (halaman belum tersedia)">Persamaan Hamilton–Jacobi</a><br><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Persamaan_gerak_Appell&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Persamaan gerak Appell (halaman belum tersedia)">Persamaan gerak Appell</a><br><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Persamaan_Udwadia%E2%80%93Kalaba&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Persamaan Udwadia–Kalaba (halaman belum tersedia)">Persamaan Udwadia–Kalaba</a> </div> </div></li> </ul> </div> </div></td> </tr> <tr> <td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"> <div class="sidebar-list-title" style="background:#ddf;text-align:center;"> Topik inti </div> <div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"> <div class="hlist" style="margin-left: 0em;"> <ul> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Benda_tegar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Benda tegar">Benda tegar</a> <ul> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Dinamika_benda_tegar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Dinamika benda tegar">dinamika</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Persamaan_Euler_(dinamika_benda_tegar)&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Persamaan Euler (dinamika benda tegar) (halaman belum tersedia)">persamaan Euler</a></li> </ul></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gaya_gesek?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gaya gesek">Friksi</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gaya_fiksi?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Gaya fiksi">Gaya fiksi</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gerak">Gerak</a> (<a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_lurus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gerak lurus">linear</a>)</li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_harmonik_sederhana?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gerak harmonik sederhana">Gerak harmonik sederhana</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Getaran?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Getaran">Getaran</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Hukum_gerak_Euler?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Hukum gerak Euler"><span style="white-space: normal;">Hukum gerak Euler</span></a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Hukum_gerak_Newton?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Hukum gerak Newton">Hukum gerak Newton</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Hukum_gravitasi_universal_Newton?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Hukum gravitasi universal Newton"><span style="white-space: normal;">Hukum gravitasi universal Newton</span></a></li> <li><span class="nowrap"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Kerangka_acuan_inersia?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kerangka acuan inersia">Inersia</a> / <a href="https://id-m-wikipedia-org.translate.goog/wiki/Kerangka_acuan_non-inersia?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Kerangka acuan non-inersia">Kerangka acuan non-inersia</a></span></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Kecepatan_relatif?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kecepatan relatif">Kecepatan relatif</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Mekanika_gerak_partikel_planar&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Mekanika gerak partikel planar (halaman belum tersedia)">Mekanika gerak partikel planar</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Osilator_harmonis&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Osilator harmonis (halaman belum tersedia)">Osilator harmonis</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Peredaman&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Peredaman (halaman belum tersedia)">Peredaman</a> (<a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Rasio_peredaman&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Rasio peredaman (halaman belum tersedia)">rasio</a>)</li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Perpindahan?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Perpindahan">Perpindahan</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Persamaan_gerak&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Persamaan gerak (halaman belum tersedia)">Persamaan gerak</a></li> </ul> </div> </div> </div></td> </tr> <tr> <td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"> <div class="sidebar-list-title" style="background:#ddf;text-align:center;"> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Rotasi_mengelilingi_sumbu_tetap?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Rotasi mengelilingi sumbu tetap">Rotasi</a> </div> <div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"> <div class="hlist" style="margin-left: 0em;"> <ul> <li><a class="mw-selflink selflink">Gerak melingkar</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Kerangka_acuan_berotasi&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Kerangka acuan berotasi (halaman belum tersedia)">Kerangka acuan berotasi</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gaya_sentripetal?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gaya sentripetal">Gaya sentripetal</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gaya_sentrifugal?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gaya sentrifugal">Gaya sentrifugal</a> <ul> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gaya_sentrifugal_reaktif&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Gaya sentrifugal reaktif (halaman belum tersedia)">reaktif</a></li> </ul></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Efek_coriolis?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Efek coriolis">Gaya coriolis</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Pendulum_(matematika)&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Pendulum (matematika) (halaman belum tersedia)">Pendulum</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Kecepatan?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Kecepatan_tangensial" title="Kecepatan">Kecepatan tangensial</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Kecepatan_putar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Kecepatan putar">Kecepatan putar</a></li> </ul> </div> <ul> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Percepatan_sudut?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Percepatan sudut">Percepatan sudut</a> / <a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Perpindahan_sudut&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Perpindahan sudut (halaman belum tersedia)">perpindahan</a> / <a href="https://id-m-wikipedia-org.translate.goog/wiki/Frekuensi_sudut?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Frekuensi sudut">frekuensi</a> / <a href="https://id-m-wikipedia-org.translate.goog/wiki/Kecepatan_sudut?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kecepatan sudut">kecepatan</a></li> </ul> </div> </div></td> </tr> <tr> <td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"> <div class="sidebar-list-title" style="background:#ddf;text-align:center;"> Ilmuwan </div> <div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0.35em;"> <div class="hlist" style="margin-left: 0em;"> <ul> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Galileo_Galilei?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Galileo Galilei">Galileo</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Isaac_Newton?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Isaac Newton">Newton</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Johannes_Kepler?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Johannes Kepler">Kepler</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Jeremiah_Horrocks?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Jeremiah Horrocks">Horrocks</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Edmond_Halley?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Edmond Halley">Halley</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Leonhard_Euler?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Leonhard Euler">Euler</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Jean_le_Rond_d%27Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Jean le Rond d'Alembert">d'Alembert</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Alexis_Clairaut?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Alexis Clairaut">Clairaut</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Joseph-Louis_Lagrange?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Joseph-Louis Lagrange">Lagrange</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Pierre-Simon_Laplace?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Pierre-Simon Laplace">Laplace</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/William_Rowan_Hamilton?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="William Rowan Hamilton">Hamilton</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Sim%C3%A9on_Denis_Poisson?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Daniel_Bernoulli?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Daniel Bernoulli">Daniel Bernoulli</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Johann_Bernoulli?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Johann Bernoulli">Johann Bernoulli</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Augustin-Louis_Cauchy?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Augustin-Louis Cauchy">Cauchy</a></li> </ul> </div> </div> </div></td> </tr> <tr> <td class="sidebar-navbar" style="padding-top:0.15em;"><style data-mw-deduplicate="TemplateStyles:r18590415">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}.mw-parser-output .infobox .navbar{font-size:100%}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style> <div class="navbar plainlinks hlist navbar-mini"> <ul> <li class="nv-lihat"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Templat:Mekanika_klasik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Templat:Mekanika klasik"><abbr title="Lihat templat ini">l</abbr></a></li> <li class="nv-bicara"><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Pembicaraan_Templat:Mekanika_klasik&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Pembicaraan Templat:Mekanika klasik (halaman belum tersedia)"><abbr title="Diskusikan templat ini">b</abbr></a></li> <li class="nv-sunting"><a class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://id.wikipedia.org/w/index.php?title%3DTemplat:Mekanika_klasik%26action%3Dedit"><abbr title="Sunting templat ini">s</abbr></a></li> </ul> </div></td> </tr> </tbody> </table> <p><b>Gerak melingkar</b> (<a href="https://id-m-wikipedia-org.translate.goog/wiki/Bahasa_Inggris?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Bahasa Inggris">bahasa Inggris</a>: <span lang="en"><i>circular motion</i></span>) adalah gerak suatu <a href="https://id-m-wikipedia-org.translate.goog/wiki/Benda?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Benda">benda</a> yang membentuk lintasan berupa <a href="https://id-m-wikipedia-org.translate.goog/wiki/Lingkaran?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Lingkaran">lingkaran</a> mengelilingi suatu titik tetap. Agar suatu benda dapat bergerak melingkar ia membutuhkan adanya <a href="https://id-m-wikipedia-org.translate.goog/wiki/Gaya?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-disambig" title="Gaya">gaya</a> yang selalu <i>membelokkan</i>-nya menuju pusat lintasan lingkaran. Gaya ini dinamakan <a href="https://id-m-wikipedia-org.translate.goog/wiki/Gaya_sentripetal?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gaya sentripetal">gaya sentripetal</a>. Suatu gerak melingkar beraturan dapat dikatakan sebagai suatu gerak dipercepat beraturan, mengingat perlu adanya suatu <a href="https://id-m-wikipedia-org.translate.goog/wiki/Percepatan?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Percepatan">percepatan</a> yang besarnya tetap dengan arah yang berubah, yang selalu mengubah arah gerak benda agar menempuh lintasan berbentuk lingkaran.<sup id="cite_ref-1" class="reference"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></p> <figure class="mw-halign-right" typeof="mw:File/Thumb"> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Berkas:Circular_motion_diagram.png?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Circular_motion_diagram.png/180px-Circular_motion_diagram.png" decoding="async" width="180" height="189" class="mw-file-element" srcset="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/7/7b/Circular_motion_diagram.png 1.5x" data-file-width="255" data-file-height="268"></a> <figcaption> Gerak melingkar. </figcaption> </figure> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"> <input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"> <div class="toctitle" lang="id" dir="ltr"> <h2 id="mw-toc-heading">Daftar isi</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span> </div> <ul> <li class="toclevel-1 tocsection-1"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Besaran_gerak_melingkar"><span class="tocnumber">1</span> <span class="toctext">Besaran gerak melingkar</span></a> <ul> <li class="toclevel-2 tocsection-2"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Turunan_dan_integral"><span class="tocnumber">1.1</span> <span class="toctext">Turunan dan integral</span></a></li> <li class="toclevel-2 tocsection-3"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Hubungan_antar_besaran_sudut_dan_tangensial"><span class="tocnumber">1.2</span> <span class="toctext">Hubungan antar besaran sudut dan tangensial</span></a></li> </ul></li> <li class="toclevel-1 tocsection-4"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Jenis_gerak_melingkar"><span class="tocnumber">2</span> <span class="toctext">Jenis gerak melingkar</span></a> <ul> <li class="toclevel-2 tocsection-5"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Gerak_melingkar_beraturan"><span class="tocnumber">2.1</span> <span class="toctext">Gerak melingkar beraturan</span></a></li> <li class="toclevel-2 tocsection-6"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Gerak_melingkar_berubah_beraturan"><span class="tocnumber">2.2</span> <span class="toctext">Gerak melingkar berubah beraturan</span></a></li> </ul></li> <li class="toclevel-1 tocsection-7"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Persamaan_parametrik"><span class="tocnumber">3</span> <span class="toctext">Persamaan parametrik</span></a> <ul> <li class="toclevel-2 tocsection-8"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Hubungan_antar_besaran_linier_dan_angular"><span class="tocnumber">3.1</span> <span class="toctext">Hubungan antar besaran linier dan angular</span></a></li> <li class="toclevel-2 tocsection-9"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Kecepatan_tangensial_dan_kecepatan_sudut"><span class="tocnumber">3.2</span> <span class="toctext">Kecepatan tangensial dan kecepatan sudut</span></a></li> <li class="toclevel-2 tocsection-10"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Percepatan_tangensial_dan_kecepatan_sudut"><span class="tocnumber">3.3</span> <span class="toctext">Percepatan tangensial dan kecepatan sudut</span></a></li> <li class="toclevel-2 tocsection-11"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Kecepatan_sudut_tidak_tetap"><span class="tocnumber">3.4</span> <span class="toctext">Kecepatan sudut tidak tetap</span></a> <ul> <li class="toclevel-3 tocsection-12"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Kecepatan_sudut"><span class="tocnumber">3.4.1</span> <span class="toctext">Kecepatan sudut</span></a></li> </ul></li> </ul></li> <li class="toclevel-1 tocsection-13"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Gerak_berubah_beraturan"><span class="tocnumber">4</span> <span class="toctext">Gerak berubah beraturan</span></a></li> <li class="toclevel-1 tocsection-14"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Lihat_pula"><span class="tocnumber">5</span> <span class="toctext">Lihat pula</span></a></li> <li class="toclevel-1 tocsection-15"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Referensi"><span class="tocnumber">6</span> <span class="toctext">Referensi</span></a></li> <li class="toclevel-1 tocsection-16"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Pranala_luar"><span class="tocnumber">7</span> <span class="toctext">Pranala luar</span></a></li> </ul> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Besaran_gerak_melingkar">Besaran gerak melingkar</h2><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Besaran gerak melingkar" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <section class="mf-section-1 collapsible-block" id="mf-section-1"> <p>Besaran-besaran yang mendeskripsikan suatu gerak melingkar adalah <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> θ </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \theta \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4648910623b113399a15dc3065ab747ea127b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.371ex; width:1.074ex; height:2.176ex;" alt="{\displaystyle \theta \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.074ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4648910623b113399a15dc3065ab747ea127b5" data-alt="{\displaystyle \theta \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.404ex; height:1.676ex;" alt="{\displaystyle \omega \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.404ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" data-alt="{\displaystyle \omega \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> α </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \alpha \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63fb046fc5e294f95686e8e90977c4280e5336b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.301ex; width:1.402ex; height:1.676ex;" alt="{\displaystyle \alpha \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.402ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63fb046fc5e294f95686e8e90977c4280e5336b8" data-alt="{\displaystyle \alpha \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> atau berturur-turut berarti sudut, kecepatan sudut dan percepatan sudut. Besaran-besaran ini bila dianalogikan dengan gerak linier setara dengan posisi, kecepatan dan percepatan atau dilambangkan berturut-turut dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> r </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/738e0cc81ec00b6037431a976a450a9499e90803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.338ex; width:1ex; height:1.676ex;" alt="{\displaystyle r\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/738e0cc81ec00b6037431a976a450a9499e90803" data-alt="{\displaystyle r\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> v </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21de446e92118ae9e636f1152b95eb370601fad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.086ex; height:1.676ex;" alt="{\displaystyle v\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.086ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21de446e92118ae9e636f1152b95eb370601fad" data-alt="{\displaystyle v\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> a </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/960d706f1d2cca91fe2d504d0c51a1ae6173e2e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.334ex; width:1.176ex; height:1.676ex;" alt="{\displaystyle a\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.176ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/960d706f1d2cca91fe2d504d0c51a1ae6173e2e2" data-alt="{\displaystyle a\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>.</p> <table class="wikitable" style="text-align: center;"> <caption> Besaran gerak lurus dan melingkar </caption> <tbody> <tr> <th colspan="2">Gerak lurus</th> <th>Gerak melingkar</th> </tr> <tr> <th width="120"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Besaran?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Besaran">Besaran</a></th> <th width="120">Satuan (<a href="https://id-m-wikipedia-org.translate.goog/wiki/SI_(satuan_ukur)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="SI (satuan ukur)">SI</a>)</th> <th width="120">Satuan (<a href="https://id-m-wikipedia-org.translate.goog/wiki/SI_(satuan_ukur)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="SI (satuan ukur)">SI</a>)</th> </tr> <tr> <td>posisi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> r </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/738e0cc81ec00b6037431a976a450a9499e90803" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.338ex; width:1ex; height:1.676ex;" alt="{\displaystyle r\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/738e0cc81ec00b6037431a976a450a9499e90803" data-alt="{\displaystyle r\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> <td><a href="https://id-m-wikipedia-org.translate.goog/wiki/Meter?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Meter">m</a></td> <td>rad</td> </tr> <tr> <td>kecepatan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> v </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21de446e92118ae9e636f1152b95eb370601fad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.086ex; height:1.676ex;" alt="{\displaystyle v\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.086ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21de446e92118ae9e636f1152b95eb370601fad" data-alt="{\displaystyle v\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> <td><a href="https://id-m-wikipedia-org.translate.goog/wiki/Meter?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Meter">m</a>/<a href="https://id-m-wikipedia-org.translate.goog/wiki/Detik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Detik">s</a></td> <td><a href="https://id-m-wikipedia-org.translate.goog/wiki/Radian?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Radian">rad</a>/<a href="https://id-m-wikipedia-org.translate.goog/wiki/Detik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Detik">s</a></td> </tr> <tr> <td>percepatan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> a </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/960d706f1d2cca91fe2d504d0c51a1ae6173e2e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.334ex; width:1.176ex; height:1.676ex;" alt="{\displaystyle a\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.176ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/960d706f1d2cca91fe2d504d0c51a1ae6173e2e2" data-alt="{\displaystyle a\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> <td><a href="https://id-m-wikipedia-org.translate.goog/wiki/Meter?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Meter">m</a>/<a href="https://id-m-wikipedia-org.translate.goog/wiki/Detik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Detik">s</a><sup>2</sup></td> <td><a href="https://id-m-wikipedia-org.translate.goog/wiki/Radian?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Radian">rad</a>/<a href="https://id-m-wikipedia-org.translate.goog/wiki/Detik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Detik">s</a><sup>2</sup></td> </tr> <tr> <td>-</td> <td>-</td> <td><a href="https://id-m-wikipedia-org.translate.goog/wiki/Detik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Detik">s</a></td> </tr> <tr> <td>-</td> <td>-</td> <td><a href="https://id-m-wikipedia-org.translate.goog/wiki/Meter?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Meter">m</a></td> </tr> </tbody> </table> <div class="mw-heading mw-heading3"> <h3 id="Turunan_dan_integral">Turunan dan integral</h3><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=2&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Turunan dan integral" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <p>Seperti halnya kembarannya dalam gerak linier, besaran-besaran gerak melingkar pun memiliki hubungan satu sama lain melalui proses integrasi dan diferensiasi.</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \omega \ dt=\theta \quad \leftrightarrow \quad \omega ={\frac {d\theta }{dt}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo> ∫ </mo> <mi> ω </mi> <mtext>   </mtext> <mi> d </mi> <mi> t </mi> <mo> = </mo> <mi> θ </mi> <mspace width="1em"></mspace> <mo stretchy="false"> ↔ </mo> <mspace width="1em"></mspace> <mi> ω </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mi> θ </mi> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \int \omega \ dt=\theta \quad \leftrightarrow \quad \omega ={\frac {d\theta }{dt}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b9f83f83e75db9ed5a3bfb401bb9f7e51eaeae2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:26.798ex; height:5.843ex;" alt="{\displaystyle \int \omega \ dt=\theta \quad \leftrightarrow \quad \omega ={\frac {d\theta }{dt}}}"> </noscript><span class="lazy-image-placeholder" style="width: 26.798ex;height: 5.843ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b9f83f83e75db9ed5a3bfb401bb9f7e51eaeae2" data-alt="{\displaystyle \int \omega \ dt=\theta \quad \leftrightarrow \quad \omega ={\frac {d\theta }{dt}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \alpha \ dt=\omega \quad \leftrightarrow \quad \alpha ={\frac {d\omega }{dt}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo> ∫ </mo> <mi> α </mi> <mtext>   </mtext> <mi> d </mi> <mi> t </mi> <mo> = </mo> <mi> ω </mi> <mspace width="1em"></mspace> <mo stretchy="false"> ↔ </mo> <mspace width="1em"></mspace> <mi> α </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mi> ω </mi> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \int \alpha \ dt=\omega \quad \leftrightarrow \quad \alpha ={\frac {d\omega }{dt}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2be288f110462b31bfd90970b64ec3e72f3c524" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.592ex; height:5.843ex;" alt="{\displaystyle \int \alpha \ dt=\omega \quad \leftrightarrow \quad \alpha ={\frac {d\omega }{dt}}}"> </noscript><span class="lazy-image-placeholder" style="width: 27.592ex;height: 5.843ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2be288f110462b31bfd90970b64ec3e72f3c524" data-alt="{\displaystyle \int \alpha \ dt=\omega \quad \leftrightarrow \quad \alpha ={\frac {d\omega }{dt}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \int \alpha \ dt^{2}=\theta \quad \leftrightarrow \quad \alpha ={\frac {d^{2}\theta }{dt^{2}}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo> ∫ </mo> <mo> ∫ </mo> <mi> α </mi> <mtext>   </mtext> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> = </mo> <mi> θ </mi> <mspace width="1em"></mspace> <mo stretchy="false"> ↔ </mo> <mspace width="1em"></mspace> <mi> α </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> θ </mi> </mrow> <mrow> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \int \int \alpha \ dt^{2}=\theta \quad \leftrightarrow \quad \alpha ={\frac {d^{2}\theta }{dt^{2}}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48918dc357f44adaca0052adeb2b67dcd0ad421b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:31.573ex; height:6.176ex;" alt="{\displaystyle \int \int \alpha \ dt^{2}=\theta \quad \leftrightarrow \quad \alpha ={\frac {d^{2}\theta }{dt^{2}}}}"> </noscript><span class="lazy-image-placeholder" style="width: 31.573ex;height: 6.176ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48918dc357f44adaca0052adeb2b67dcd0ad421b" data-alt="{\displaystyle \int \int \alpha \ dt^{2}=\theta \quad \leftrightarrow \quad \alpha ={\frac {d^{2}\theta }{dt^{2}}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <div class="mw-heading mw-heading3"> <h3 id="Hubungan_antar_besaran_sudut_dan_tangensial">Hubungan antar besaran sudut dan tangensial</h3><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=3&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Hubungan antar besaran sudut dan tangensial" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <p>Antara besaran gerak linier dan melingkar terdapat suatu hubungan melalui <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> R </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle R\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d91a7cdaf18b7e9db06c3ef959015614820c0e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.378ex; width:1.755ex; height:2.176ex;" alt="{\displaystyle R\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.755ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d91a7cdaf18b7e9db06c3ef959015614820c0e7" data-alt="{\displaystyle R\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> khusus untuk komponen tangensial, yaitu</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta ={\frac {r_{T}}{R}}\ \,\ \ \omega ={\frac {v_{T}}{R}}\ \,\ \ \alpha ={\frac {a_{T}}{R}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> θ </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mi> R </mi> </mfrac> </mrow> <mtext>   </mtext> <mspace width="thinmathspace"></mspace> <mtext>   </mtext> <mtext>   </mtext> <mi> ω </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mi> R </mi> </mfrac> </mrow> <mtext>   </mtext> <mspace width="thinmathspace"></mspace> <mtext>   </mtext> <mtext>   </mtext> <mi> α </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mi> R </mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \theta ={\frac {r_{T}}{R}}\ \,\ \ \omega ={\frac {v_{T}}{R}}\ \,\ \ \alpha ={\frac {a_{T}}{R}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c54d109f63ad1f52fbfd61440097634a8768ace0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:27.66ex; height:4.843ex;" alt="{\displaystyle \theta ={\frac {r_{T}}{R}}\ \,\ \ \omega ={\frac {v_{T}}{R}}\ \,\ \ \alpha ={\frac {a_{T}}{R}}}"> </noscript><span class="lazy-image-placeholder" style="width: 27.66ex;height: 4.843ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c54d109f63ad1f52fbfd61440097634a8768ace0" data-alt="{\displaystyle \theta ={\frac {r_{T}}{R}}\ \,\ \ \omega ={\frac {v_{T}}{R}}\ \,\ \ \alpha ={\frac {a_{T}}{R}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>Perhatikan bahwa di sini digunakan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{T}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r_{T}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b521c1acc9e9b85da325f25a7d1b380cdb1d0a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.438ex; height:2.009ex;" alt="{\displaystyle r_{T}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.438ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b521c1acc9e9b85da325f25a7d1b380cdb1d0a2" data-alt="{\displaystyle r_{T}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> yang didefinisikan sebagai jarak yang ditempuh atau tali busur yang telah dilewati dalam suatu selang waktu dan bukan hanya posisi pada suatu saat, yaitu</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{T}\approx |{\overrightarrow {r}}(t+\Delta t)-{\overrightarrow {r}}(t)|\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo> ≈ </mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> r </mi> <mo> → </mo> </mover> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo> + </mo> <mi mathvariant="normal"> Δ </mi> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> − </mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> r </mi> <mo> → </mo> </mover> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r_{T}\approx |{\overrightarrow {r}}(t+\Delta t)-{\overrightarrow {r}}(t)|\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30f584c7d4ad573318ab1047d44cf1a3e8c82952" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.111ex; width:25.214ex; height:3.509ex;" alt="{\displaystyle r_{T}\approx |{\overrightarrow {r}}(t+\Delta t)-{\overrightarrow {r}}(t)|\!}"> </noscript><span class="lazy-image-placeholder" style="width: 25.214ex;height: 3.509ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30f584c7d4ad573318ab1047d44cf1a3e8c82952" data-alt="{\displaystyle r_{T}\approx |{\overrightarrow {r}}(t+\Delta t)-{\overrightarrow {r}}(t)|\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>untuk suatu selang waktu kecil atau sudut yang sempit.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Jenis_gerak_melingkar">Jenis gerak melingkar</h2><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=4&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Jenis gerak melingkar" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <section class="mf-section-2 collapsible-block" id="mf-section-2"> <p>Gerak melingkar dapat dibedakan menjadi dua jenis, atas keseragaman kecepatan sudutnya <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.404ex; height:1.676ex;" alt="{\displaystyle \omega \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.404ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" data-alt="{\displaystyle \omega \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, yaitu:</p> <ul> <li>gerak melingkar beraturan, dan</li> <li>gerak melingkar berubah beraturan.</li> </ul> <div class="mw-heading mw-heading3"> <h3 id="Gerak_melingkar_beraturan">Gerak melingkar beraturan</h3><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=5&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Gerak melingkar beraturan" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <p>Gerak Melingkar Beraturan (<b>GMB</b>) adalah gerak melingkar dengan besar kecepatan sudut <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.404ex; height:1.676ex;" alt="{\displaystyle \omega \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.404ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" data-alt="{\displaystyle \omega \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> tetap. Besar Kecepatan sudut diperolah dengan membagi kecepatan tangensial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{T}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{T}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/557430130a7f0e6911fe985fd0b0878d795b47dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.517ex; height:2.009ex;" alt="{\displaystyle v_{T}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.517ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/557430130a7f0e6911fe985fd0b0878d795b47dc" data-alt="{\displaystyle v_{T}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> dengan jari-jari lintasan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> R </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle R\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d91a7cdaf18b7e9db06c3ef959015614820c0e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.378ex; width:1.755ex; height:2.176ex;" alt="{\displaystyle R\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.755ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d91a7cdaf18b7e9db06c3ef959015614820c0e7" data-alt="{\displaystyle R\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>.</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega ={\frac {v_{T}}{R}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mi> R </mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega ={\frac {v_{T}}{R}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f727c02ff7076a50f26c98c29e6f1c1cd92247c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.897ex; height:4.843ex;" alt="{\displaystyle \omega ={\frac {v_{T}}{R}}}"> </noscript><span class="lazy-image-placeholder" style="width: 7.897ex;height: 4.843ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f727c02ff7076a50f26c98c29e6f1c1cd92247c" data-alt="{\displaystyle \omega ={\frac {v_{T}}{R}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>Arah kecepatan linier <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> v </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21de446e92118ae9e636f1152b95eb370601fad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.086ex; height:1.676ex;" alt="{\displaystyle v\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.086ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b21de446e92118ae9e636f1152b95eb370601fad" data-alt="{\displaystyle v\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> dalam GMB selalu menyinggung lintasan, yang berarti arahnya sama dengan arah kecepatan tangensial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{T}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{T}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/557430130a7f0e6911fe985fd0b0878d795b47dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.517ex; height:2.009ex;" alt="{\displaystyle v_{T}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.517ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/557430130a7f0e6911fe985fd0b0878d795b47dc" data-alt="{\displaystyle v_{T}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>. Tetapnya nilai kecepatan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{T}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{T}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/557430130a7f0e6911fe985fd0b0878d795b47dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.517ex; height:2.009ex;" alt="{\displaystyle v_{T}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.517ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/557430130a7f0e6911fe985fd0b0878d795b47dc" data-alt="{\displaystyle v_{T}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> akibat konsekuensi dar tetapnya nilai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.404ex; height:1.676ex;" alt="{\displaystyle \omega \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.404ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" data-alt="{\displaystyle \omega \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>. Selain itu terdapat pula percepatan radial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{R}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> R </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{R}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b9da7a088d09b6e5aa136df27ce9b1a38bde45b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.709ex; height:2.009ex;" alt="{\displaystyle a_{R}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.709ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b9da7a088d09b6e5aa136df27ce9b1a38bde45b" data-alt="{\displaystyle a_{R}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> yang besarnya tetap dengan arah yang berubah. Percepatan ini disebut sebagai percepatan sentripetal, di mana arahnya selalu menunjuk ke pusat lingkaran.</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{R}={\frac {v^{2}}{R}}={\frac {v_{T}^{2}}{R}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> R </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> R </mi> </mfrac> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mi> R </mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{R}={\frac {v^{2}}{R}}={\frac {v_{T}^{2}}{R}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e7ac33fd47b0e40890668343e3bbe3a814fa4c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.277ex; height:6.176ex;" alt="{\displaystyle a_{R}={\frac {v^{2}}{R}}={\frac {v_{T}^{2}}{R}}}"> </noscript><span class="lazy-image-placeholder" style="width: 15.277ex;height: 6.176ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e7ac33fd47b0e40890668343e3bbe3a814fa4c2" data-alt="{\displaystyle a_{R}={\frac {v^{2}}{R}}={\frac {v_{T}^{2}}{R}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>Bila <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> T </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle T\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/931cff7af09ba413dbc1cecdc4a3fa818a4c20b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.636ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/931cff7af09ba413dbc1cecdc4a3fa818a4c20b4" data-alt="{\displaystyle T\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> adalah waktu yang dibutuhkan untuk menyelesaikan satu putaran penuh dalam lintasan lingkaran <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta =2\pi R\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> θ </mi> <mo> = </mo> <mn> 2 </mn> <mi> π </mi> <mi> R </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \theta =2\pi R\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5af2351dab7cf9a91452913447727cea7acfbb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.378ex; width:8.438ex; height:2.176ex;" alt="{\displaystyle \theta =2\pi R\!}"> </noscript><span class="lazy-image-placeholder" style="width: 8.438ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5af2351dab7cf9a91452913447727cea7acfbb5" data-alt="{\displaystyle \theta =2\pi R\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, maka dapat pula dituliskan</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{T}={\frac {2\pi R}{T}}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn> 2 </mn> <mi> π </mi> <mi> R </mi> </mrow> <mi> T </mi> </mfrac> </mrow> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{T}={\frac {2\pi R}{T}}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1618f48c86e02c3df8bf35d11d4ebfd317250513" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.108ex; width:10.431ex; height:5.176ex;" alt="{\displaystyle v_{T}={\frac {2\pi R}{T}}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 10.431ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1618f48c86e02c3df8bf35d11d4ebfd317250513" data-alt="{\displaystyle v_{T}={\frac {2\pi R}{T}}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>Kinematika gerak melingkar beraturan adalah</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta (t)=\theta _{0}+\omega \ t}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> θ </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> θ </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> + </mo> <mi> ω </mi> <mtext>   </mtext> <mi> t </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \theta (t)=\theta _{0}+\omega \ t} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d68400b434ef377be391fe7badfeeca1f429d31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.689ex; height:2.843ex;" alt="{\displaystyle \theta (t)=\theta _{0}+\omega \ t}"> </noscript><span class="lazy-image-placeholder" style="width: 14.689ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d68400b434ef377be391fe7badfeeca1f429d31" data-alt="{\displaystyle \theta (t)=\theta _{0}+\omega \ t}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta (t)\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> θ </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \theta (t)\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1daff54ca05d133601e714a168d8112cb66eea9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.166ex; width:3.519ex; height:2.843ex;" alt="{\displaystyle \theta (t)\!}"> </noscript><span class="lazy-image-placeholder" style="width: 3.519ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1daff54ca05d133601e714a168d8112cb66eea9" data-alt="{\displaystyle \theta (t)\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> adalah sudut yang dilalui pada suatu saat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> t </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle t\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a0802184af6ebcdd686d12c7df048f36d565dda" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.315ex; width:0.768ex; height:2.009ex;" alt="{\displaystyle t\!}"> </noscript><span class="lazy-image-placeholder" style="width: 0.768ex;height: 2.009ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a0802184af6ebcdd686d12c7df048f36d565dda" data-alt="{\displaystyle t\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta _{0}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> θ </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \theta _{0}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d9174c4e61cbf052c7dad0365b081098a7e706b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.145ex; height:2.509ex;" alt="{\displaystyle \theta _{0}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.145ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d9174c4e61cbf052c7dad0365b081098a7e706b" data-alt="{\displaystyle \theta _{0}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> adalah sudut mula-mula dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.404ex; height:1.676ex;" alt="{\displaystyle \omega \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.404ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" data-alt="{\displaystyle \omega \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> adalah kecepatan sudut (yang tetap nilainya).</p> <p>Ciri-ciri gerak melingkar beraturan:</p> <ul> <li>Besar kelajuan linearnya tetap</li> <li>Besar kecepatan sudutnya tetap</li> <li>Besar percepatan sentripetalnya tetap</li> <li>Lintasannya berupa lingkaran</li> </ul> <div class="mw-heading mw-heading3"> <h3 id="Gerak_melingkar_berubah_beraturan">Gerak melingkar berubah beraturan</h3><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=6&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Gerak melingkar berubah beraturan" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <p>Gerak Melingkar Berubah Beraturan (<b>GMBB</b>) adalah gerak melingkar dengan percepatan sudut <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> α </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \alpha \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63fb046fc5e294f95686e8e90977c4280e5336b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.301ex; width:1.402ex; height:1.676ex;" alt="{\displaystyle \alpha \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.402ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63fb046fc5e294f95686e8e90977c4280e5336b8" data-alt="{\displaystyle \alpha \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> tetap. Dalam gerak ini terdapat percepatan tangensial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{T}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{T}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5115a2822f0bc7fbd58a6f4c25a0d9b168cdcbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.619ex; height:2.009ex;" alt="{\displaystyle a_{T}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.619ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5115a2822f0bc7fbd58a6f4c25a0d9b168cdcbe" data-alt="{\displaystyle a_{T}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> (yang dalam hal ini sama dengan percepatan linier) yang menyinggung lintasan lingkaran (berhimpit dengan arah kecepatan tangensial <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{T}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{T}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/557430130a7f0e6911fe985fd0b0878d795b47dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.517ex; height:2.009ex;" alt="{\displaystyle v_{T}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.517ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/557430130a7f0e6911fe985fd0b0878d795b47dc" data-alt="{\displaystyle v_{T}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>).</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ={\frac {a_{T}}{R}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> α </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mi> R </mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \alpha ={\frac {a_{T}}{R}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d4a754818f4922092718720e6e05d5b378ca52a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.041ex; height:4.843ex;" alt="{\displaystyle \alpha ={\frac {a_{T}}{R}}}"> </noscript><span class="lazy-image-placeholder" style="width: 8.041ex;height: 4.843ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d4a754818f4922092718720e6e05d5b378ca52a" data-alt="{\displaystyle \alpha ={\frac {a_{T}}{R}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>Kinematika GMBB adalah</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega (t)=\omega _{0}+\alpha \ t\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> + </mo> <mi> α </mi> <mtext>   </mtext> <mi> t </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega (t)=\omega _{0}+\alpha \ t\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da0715d9b8406a0aeb2eaa0aa802a3873af27e4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.315ex; width:15.37ex; height:2.843ex;" alt="{\displaystyle \omega (t)=\omega _{0}+\alpha \ t\!}"> </noscript><span class="lazy-image-placeholder" style="width: 15.37ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da0715d9b8406a0aeb2eaa0aa802a3873af27e4c" data-alt="{\displaystyle \omega (t)=\omega _{0}+\alpha \ t\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta (t)=\theta _{0}+\omega _{0}\ t+{\frac {1}{2}}\alpha \ t^{2}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> θ </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> θ </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> + </mo> <msub> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mtext>   </mtext> <mi> t </mi> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mi> α </mi> <mtext>   </mtext> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \theta (t)=\theta _{0}+\omega _{0}\ t+{\frac {1}{2}}\alpha \ t^{2}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f79294359c91e83822090b4d7c7101663fa58ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:24.544ex; height:5.176ex;" alt="{\displaystyle \theta (t)=\theta _{0}+\omega _{0}\ t+{\frac {1}{2}}\alpha \ t^{2}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 24.544ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f79294359c91e83822090b4d7c7101663fa58ea" data-alt="{\displaystyle \theta (t)=\theta _{0}+\omega _{0}\ t+{\frac {1}{2}}\alpha \ t^{2}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega ^{2}(t)=\omega _{0}^{2}+2\alpha \ (\theta (t)-\theta _{0})\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msubsup> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <mn> 2 </mn> <mi> α </mi> <mtext>   </mtext> <mo stretchy="false"> ( </mo> <mi> θ </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> − </mo> <msub> <mi> θ </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega ^{2}(t)=\omega _{0}^{2}+2\alpha \ (\theta (t)-\theta _{0})\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af3aba8ba9badf82eceeba9e5f65baf38b7c51c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.166ex; width:27.132ex; height:3.343ex;" alt="{\displaystyle \omega ^{2}(t)=\omega _{0}^{2}+2\alpha \ (\theta (t)-\theta _{0})\!}"> </noscript><span class="lazy-image-placeholder" style="width: 27.132ex;height: 3.343ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af3aba8ba9badf82eceeba9e5f65baf38b7c51c4" data-alt="{\displaystyle \omega ^{2}(t)=\omega _{0}^{2}+2\alpha \ (\theta (t)-\theta _{0})\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> α </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \alpha \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63fb046fc5e294f95686e8e90977c4280e5336b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.301ex; width:1.402ex; height:1.676ex;" alt="{\displaystyle \alpha \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.402ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63fb046fc5e294f95686e8e90977c4280e5336b8" data-alt="{\displaystyle \alpha \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> adalah percepatan sudut yang bernilai tetap dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{0}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega _{0}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4f1e115a64b8991b3acf59777082e469ad71a2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.5ex; height:2.009ex;" alt="{\displaystyle \omega _{0}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.5ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4f1e115a64b8991b3acf59777082e469ad71a2e" data-alt="{\displaystyle \omega _{0}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> adalah kecepatan sudut mula-mula.</p> <p>Ciri-ciri gerak melingkar berubah beraturan:</p> <ul> <li>Besar kelajuan linearnya berubah</li> <li>Besar kecepatan sudutnya berubah</li> <li>Besar percepatan sentripetalnya berubah</li> <li>Lintasannya berupa lingkaran</li> </ul> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Persamaan_parametrik">Persamaan parametrik</h2><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=7&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Persamaan parametrik" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <section class="mf-section-3 collapsible-block" id="mf-section-3"> <p>Gerak melingkar dapat pula dinyatakan dalam persamaan parametrik dengan terlebih dahulu mendefinisikan:</p> <ul> <li>titik awal gerakan dilakukan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{0},y_{0})\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false"> ( </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> , </mo> <msub> <mi> y </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle (x_{0},y_{0})\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05fb39711ffdcd02af84b109fd4c171d5266b597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.166ex; width:7.2ex; height:2.843ex;" alt="{\displaystyle (x_{0},y_{0})\!}"> </noscript><span class="lazy-image-placeholder" style="width: 7.2ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05fb39711ffdcd02af84b109fd4c171d5266b597" data-alt="{\displaystyle (x_{0},y_{0})\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></li> <li>kecepatan sudut putaran <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.404ex; height:1.676ex;" alt="{\displaystyle \omega \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.404ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" data-alt="{\displaystyle \omega \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> (yang berarti suatu GMB)</li> <li>pusat lingkaran <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{c},y_{c})\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false"> ( </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> <mo> , </mo> <msub> <mi> y </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle (x_{c},y_{c})\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c03f03a39111ceb3f0e8aca90588100e91c262f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.166ex; width:6.98ex; height:2.843ex;" alt="{\displaystyle (x_{c},y_{c})\!}"> </noscript><span class="lazy-image-placeholder" style="width: 6.98ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c03f03a39111ceb3f0e8aca90588100e91c262f7" data-alt="{\displaystyle (x_{c},y_{c})\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></li> </ul> <p>untuk kemudian dibuat persamaannya.<sup id="cite_ref-2" class="reference"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></p> <p>Hal pertama yang harus dilakukan adalah menghitung jari-jari lintasan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> R </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle R\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d91a7cdaf18b7e9db06c3ef959015614820c0e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.378ex; width:1.755ex; height:2.176ex;" alt="{\displaystyle R\!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.755ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d91a7cdaf18b7e9db06c3ef959015614820c0e7" data-alt="{\displaystyle R\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> yang diperoleh melalui:</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R={\sqrt {(x_{0}-x_{c})^{2}+(y_{0}-y_{c})^{2}}}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> R </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false"> ( </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> − </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> <msup> <mo stretchy="false"> ) </mo> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <mo stretchy="false"> ( </mo> <msub> <mi> y </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> − </mo> <msub> <mi> y </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> <msup> <mo stretchy="false"> ) </mo> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </msqrt> </mrow> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle R={\sqrt {(x_{0}-x_{c})^{2}+(y_{0}-y_{c})^{2}}}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afe4b6888dea360b10af4bee745d253b6bb07e95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; margin-right: -0.387ex; width:30.369ex; height:4.843ex;" alt="{\displaystyle R={\sqrt {(x_{0}-x_{c})^{2}+(y_{0}-y_{c})^{2}}}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 30.369ex;height: 4.843ex;vertical-align: -1.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afe4b6888dea360b10af4bee745d253b6bb07e95" data-alt="{\displaystyle R={\sqrt {(x_{0}-x_{c})^{2}+(y_{0}-y_{c})^{2}}}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>Setelah diperoleh nilai jari-jari lintasan, persamaan dapat segera dituliskan, yaitu</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x(t)=x_{c}+R\cos(\omega t+\phi _{x})\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> x </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> <mo> + </mo> <mi> R </mi> <mi> cos </mi> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle x(t)=x_{c}+R\cos(\omega t+\phi _{x})\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5d6128177a05706d3fdda71913895eb0b37e1bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.166ex; width:26.726ex; height:2.843ex;" alt="{\displaystyle x(t)=x_{c}+R\cos(\omega t+\phi _{x})\!}"> </noscript><span class="lazy-image-placeholder" style="width: 26.726ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5d6128177a05706d3fdda71913895eb0b37e1bd" data-alt="{\displaystyle x(t)=x_{c}+R\cos(\omega t+\phi _{x})\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(t)=y_{c}+R\sin(\omega t+\phi _{y})\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> y </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> y </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> <mo> + </mo> <mi> R </mi> <mi> sin </mi> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle y(t)=y_{c}+R\sin(\omega t+\phi _{y})\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f384a6aed7adff8738fce012b74849b1b2327e65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.166ex; width:25.983ex; height:3.009ex;" alt="{\displaystyle y(t)=y_{c}+R\sin(\omega t+\phi _{y})\!}"> </noscript><span class="lazy-image-placeholder" style="width: 25.983ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f384a6aed7adff8738fce012b74849b1b2327e65" data-alt="{\displaystyle y(t)=y_{c}+R\sin(\omega t+\phi _{y})\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>dengan dua konstanta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{x}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \phi _{x}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8123e8ef144abd6c1ea988c56f64f8827b9152a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.558ex; height:2.509ex;" alt="{\displaystyle \phi _{x}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.558ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8123e8ef144abd6c1ea988c56f64f8827b9152a9" data-alt="{\displaystyle \phi _{x}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{y}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \phi _{y}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2528113e57c9c451438e8ffac7b114297c3e71e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:2.435ex; height:2.843ex;" alt="{\displaystyle \phi _{y}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.435ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2528113e57c9c451438e8ffac7b114297c3e71e" data-alt="{\displaystyle \phi _{y}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> yang masih harus ditentukan nilainya. Dengan persyaratan sebelumnya, yaitu diketahuinya nilai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{0},y_{0})\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false"> ( </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> , </mo> <msub> <mi> y </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle (x_{0},y_{0})\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05fb39711ffdcd02af84b109fd4c171d5266b597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.166ex; width:7.2ex; height:2.843ex;" alt="{\displaystyle (x_{0},y_{0})\!}"> </noscript><span class="lazy-image-placeholder" style="width: 7.2ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05fb39711ffdcd02af84b109fd4c171d5266b597" data-alt="{\displaystyle (x_{0},y_{0})\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, maka dapat ditentukan nilai <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{x}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \phi _{x}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8123e8ef144abd6c1ea988c56f64f8827b9152a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.558ex; height:2.509ex;" alt="{\displaystyle \phi _{x}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.558ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8123e8ef144abd6c1ea988c56f64f8827b9152a9" data-alt="{\displaystyle \phi _{x}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{y}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \phi _{y}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2528113e57c9c451438e8ffac7b114297c3e71e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:2.435ex; height:2.843ex;" alt="{\displaystyle \phi _{y}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.435ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2528113e57c9c451438e8ffac7b114297c3e71e" data-alt="{\displaystyle \phi _{y}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>:</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{x}=\arccos \left({\frac {x_{0}-x_{c}}{R}}\right)\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> = </mo> <mi> arccos </mi> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> − </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> </mrow> <mi> R </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \phi _{x}=\arccos \left({\frac {x_{0}-x_{c}}{R}}\right)\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09d29a3e034c24b06a80a1dc4a7104e8370ea71a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.242ex; height:6.176ex;" alt="{\displaystyle \phi _{x}=\arccos \left({\frac {x_{0}-x_{c}}{R}}\right)\!}"> </noscript><span class="lazy-image-placeholder" style="width: 23.242ex;height: 6.176ex;vertical-align: -2.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09d29a3e034c24b06a80a1dc4a7104e8370ea71a" data-alt="{\displaystyle \phi _{x}=\arccos \left({\frac {x_{0}-x_{c}}{R}}\right)\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{y}=\arcsin \left({\frac {y_{0}-y_{c}}{R}}\right)\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo> = </mo> <mi> arcsin </mi> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi> y </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> − </mo> <msub> <mi> y </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> </mrow> <mi> R </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \phi _{y}=\arcsin \left({\frac {y_{0}-y_{c}}{R}}\right)\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/872dd267064c2ea21a50198a9bffc3bd1e9414a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.483ex; height:6.176ex;" alt="{\displaystyle \phi _{y}=\arcsin \left({\frac {y_{0}-y_{c}}{R}}\right)\!}"> </noscript><span class="lazy-image-placeholder" style="width: 22.483ex;height: 6.176ex;vertical-align: -2.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/872dd267064c2ea21a50198a9bffc3bd1e9414a3" data-alt="{\displaystyle \phi _{y}=\arcsin \left({\frac {y_{0}-y_{c}}{R}}\right)\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>Perlu diketahui bahwa sebenarnya</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi _{x}=\phi _{y}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> = </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \phi _{x}=\phi _{y}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08b5943db5fd087f7f15dcd3e713083ee7302beb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:8.091ex; height:2.843ex;" alt="{\displaystyle \phi _{x}=\phi _{y}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 8.091ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08b5943db5fd087f7f15dcd3e713083ee7302beb" data-alt="{\displaystyle \phi _{x}=\phi _{y}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>karena merupakan sudut awal gerak melingkar.</p> <div class="mw-heading mw-heading3"> <h3 id="Hubungan_antar_besaran_linier_dan_angular">Hubungan antar besaran linier dan angular</h3><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=8&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Hubungan antar besaran linier dan angular" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <p>Dengan menggunakan persamaan parametrik, telah dibatasi bahwa besaran linier yang digunakan hanyalah besaran tangensial atau hanya komponen vektor pada arah angular, yang berarti tidak ada komponen vektor dalam arah radial. Dengan batasan ini hubungan antara besaran linier (tangensial) dan angular dapat dengan mudah diturunkan.</p> <div class="mw-heading mw-heading3"> <h3 id="Kecepatan_tangensial_dan_kecepatan_sudut">Kecepatan tangensial dan kecepatan sudut</h3><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=9&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Kecepatan tangensial dan kecepatan sudut" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <p>Kecepatan linier total dapat diperoleh melalui</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v={\sqrt {v_{x}^{2}+v_{y}^{2}}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> v </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <msubsup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v={\sqrt {v_{x}^{2}+v_{y}^{2}}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1d271633083813ead27235b55db3db3558cfd87" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.872ex; height:4.843ex;" alt="{\displaystyle v={\sqrt {v_{x}^{2}+v_{y}^{2}}}}"> </noscript><span class="lazy-image-placeholder" style="width: 13.872ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1d271633083813ead27235b55db3db3558cfd87" data-alt="{\displaystyle v={\sqrt {v_{x}^{2}+v_{y}^{2}}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>dan karena batasan implementasi persamaan parametrik pada gerak melingkar, maka</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{T}=v={\sqrt {v_{x}^{2}+v_{y}^{2}}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo> = </mo> <mi> v </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <msubsup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{T}=v={\sqrt {v_{x}^{2}+v_{y}^{2}}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb9e2731fd92e27cb66ed26396ed910a41e33db6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.488ex; height:4.843ex;" alt="{\displaystyle v_{T}=v={\sqrt {v_{x}^{2}+v_{y}^{2}}}}"> </noscript><span class="lazy-image-placeholder" style="width: 19.488ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb9e2731fd92e27cb66ed26396ed910a41e33db6" data-alt="{\displaystyle v_{T}=v={\sqrt {v_{x}^{2}+v_{y}^{2}}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>dengan</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{x}={\dot {x}}={\frac {dx}{dt}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> x </mi> <mo> ˙ </mo> </mover> </mrow> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mi> x </mi> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{x}={\dot {x}}={\frac {dx}{dt}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/563a2b9b25cd92686b6130fc115e8725c4f7f7c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.208ex; height:5.509ex;" alt="{\displaystyle v_{x}={\dot {x}}={\frac {dx}{dt}}}"> </noscript><span class="lazy-image-placeholder" style="width: 13.208ex;height: 5.509ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/563a2b9b25cd92686b6130fc115e8725c4f7f7c2" data-alt="{\displaystyle v_{x}={\dot {x}}={\frac {dx}{dt}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{y}={\dot {y}}={\frac {dy}{dt}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> y </mi> <mo> ˙ </mo> </mover> </mrow> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mi> y </mi> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{y}={\dot {y}}={\frac {dy}{dt}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4411370ff16458c6bb33ba74115487fa3bc9a2bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.884ex; height:5.509ex;" alt="{\displaystyle v_{y}={\dot {y}}={\frac {dy}{dt}}}"> </noscript><span class="lazy-image-placeholder" style="width: 12.884ex;height: 5.509ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4411370ff16458c6bb33ba74115487fa3bc9a2bd" data-alt="{\displaystyle v_{y}={\dot {y}}={\frac {dy}{dt}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>diperoleh</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{x}=-\omega R\sin(\omega t+\phi _{x})\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> = </mo> <mo> − </mo> <mi> ω </mi> <mi> R </mi> <mi> sin </mi> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{x}=-\omega R\sin(\omega t+\phi _{x})\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ccc10ea56898a0ad35d45c8e1905a5ad7f5fafea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.166ex; width:22.932ex; height:2.843ex;" alt="{\displaystyle v_{x}=-\omega R\sin(\omega t+\phi _{x})\!}"> </noscript><span class="lazy-image-placeholder" style="width: 22.932ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ccc10ea56898a0ad35d45c8e1905a5ad7f5fafea" data-alt="{\displaystyle v_{x}=-\omega R\sin(\omega t+\phi _{x})\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{y}=\omega R\cos(\omega t+\phi _{x})\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo> = </mo> <mi> ω </mi> <mi> R </mi> <mi> cos </mi> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{y}=\omega R\cos(\omega t+\phi _{x})\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7757837b6ba98ede1fee29a6cb7a3c2c2e5f2a2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.166ex; width:21.256ex; height:3.009ex;" alt="{\displaystyle v_{y}=\omega R\cos(\omega t+\phi _{x})\!}"> </noscript><span class="lazy-image-placeholder" style="width: 21.256ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7757837b6ba98ede1fee29a6cb7a3c2c2e5f2a2f" data-alt="{\displaystyle v_{y}=\omega R\cos(\omega t+\phi _{x})\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>sehingga</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{T}={\sqrt {(-\omega )^{2}R^{2}\sin ^{2}(\omega t+\phi _{x})+\omega ^{2}R^{2}\cos ^{2}(\omega t+\phi _{x})}}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false"> ( </mo> <mo> − </mo> <mi> ω </mi> <msup> <mo stretchy="false"> ) </mo> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <msup> <mi> R </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <msup> <mi> sin </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> + </mo> <msup> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <msup> <mi> R </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <msup> <mi> cos </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> </msqrt> </mrow> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{T}={\sqrt {(-\omega )^{2}R^{2}\sin ^{2}(\omega t+\phi _{x})+\omega ^{2}R^{2}\cos ^{2}(\omega t+\phi _{x})}}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8dac5b16257b14a58bdb3e919455b548c5a9206" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; margin-right: -0.387ex; width:52.869ex; height:4.843ex;" alt="{\displaystyle v_{T}={\sqrt {(-\omega )^{2}R^{2}\sin ^{2}(\omega t+\phi _{x})+\omega ^{2}R^{2}\cos ^{2}(\omega t+\phi _{x})}}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 52.869ex;height: 4.843ex;vertical-align: -1.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8dac5b16257b14a58bdb3e919455b548c5a9206" data-alt="{\displaystyle v_{T}={\sqrt {(-\omega )^{2}R^{2}\sin ^{2}(\omega t+\phi _{x})+\omega ^{2}R^{2}\cos ^{2}(\omega t+\phi _{x})}}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{T}=\omega R{\sqrt {\sin ^{2}(\omega t+\phi _{x})+\cos ^{2}(\omega t+\phi _{x})}}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo> = </mo> <mi> ω </mi> <mi> R </mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi> sin </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> + </mo> <msup> <mi> cos </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> </msqrt> </mrow> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{T}=\omega R{\sqrt {\sin ^{2}(\omega t+\phi _{x})+\cos ^{2}(\omega t+\phi _{x})}}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c30a712755600ba322cf29f65fbc2fab2da2a30b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; margin-right: -0.387ex; width:41.051ex; height:4.843ex;" alt="{\displaystyle v_{T}=\omega R{\sqrt {\sin ^{2}(\omega t+\phi _{x})+\cos ^{2}(\omega t+\phi _{x})}}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 41.051ex;height: 4.843ex;vertical-align: -1.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c30a712755600ba322cf29f65fbc2fab2da2a30b" data-alt="{\displaystyle v_{T}=\omega R{\sqrt {\sin ^{2}(\omega t+\phi _{x})+\cos ^{2}(\omega t+\phi _{x})}}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{T}=\omega R\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo> = </mo> <mi> ω </mi> <mi> R </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{T}=\omega R\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52952aa7bdb60d9ed5d5a99eefe0014a911342eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.378ex; width:8.816ex; height:2.509ex;" alt="{\displaystyle v_{T}=\omega R\!}"> </noscript><span class="lazy-image-placeholder" style="width: 8.816ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52952aa7bdb60d9ed5d5a99eefe0014a911342eb" data-alt="{\displaystyle v_{T}=\omega R\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <div class="mw-heading mw-heading3"> <h3 id="Percepatan_tangensial_dan_kecepatan_sudut">Percepatan tangensial dan kecepatan sudut</h3><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=10&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Percepatan tangensial dan kecepatan sudut" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <p>Dengan cara yang sama dengan sebelumnya, percepatan linier total dapat diperoleh melalui</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a={\sqrt {a_{x}^{2}+a_{y}^{2}}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> a </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <msubsup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a={\sqrt {a_{x}^{2}+a_{y}^{2}}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e595fef4ddb6cc92260aaea879fb731f0962db0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.179ex; height:4.843ex;" alt="{\displaystyle a={\sqrt {a_{x}^{2}+a_{y}^{2}}}}"> </noscript><span class="lazy-image-placeholder" style="width: 14.179ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e595fef4ddb6cc92260aaea879fb731f0962db0f" data-alt="{\displaystyle a={\sqrt {a_{x}^{2}+a_{y}^{2}}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>dan karena batasan implementasi persamaan parametrik pada gerak melingkar, maka</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{T}=a={\sqrt {a_{x}^{2}+a_{y}^{2}}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo> = </mo> <mi> a </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <msubsup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{T}=a={\sqrt {a_{x}^{2}+a_{y}^{2}}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ae0a39cd2889ae611a772f8f48c6dbec6131357" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.896ex; height:4.843ex;" alt="{\displaystyle a_{T}=a={\sqrt {a_{x}^{2}+a_{y}^{2}}}}"> </noscript><span class="lazy-image-placeholder" style="width: 19.896ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ae0a39cd2889ae611a772f8f48c6dbec6131357" data-alt="{\displaystyle a_{T}=a={\sqrt {a_{x}^{2}+a_{y}^{2}}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>dengan</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{x}={\ddot {x}}={\frac {d^{2}x}{dt^{2}}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> x </mi> <mo> ¨ </mo> </mover> </mrow> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> x </mi> </mrow> <mrow> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{x}={\ddot {x}}={\frac {d^{2}x}{dt^{2}}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c974a5da2ad4186cab4860dce3a94b05a4dbadd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.367ex; height:6.009ex;" alt="{\displaystyle a_{x}={\ddot {x}}={\frac {d^{2}x}{dt^{2}}}}"> </noscript><span class="lazy-image-placeholder" style="width: 14.367ex;height: 6.009ex;vertical-align: -2.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c974a5da2ad4186cab4860dce3a94b05a4dbadd" data-alt="{\displaystyle a_{x}={\ddot {x}}={\frac {d^{2}x}{dt^{2}}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{y}={\ddot {y}}={\frac {d^{2}y}{dt^{2}}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> y </mi> <mo> ¨ </mo> </mover> </mrow> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> y </mi> </mrow> <mrow> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{y}={\ddot {y}}={\frac {d^{2}y}{dt^{2}}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/435c2e695f8ab8be3077ba58f619789b8c546aa7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.042ex; height:6.009ex;" alt="{\displaystyle a_{y}={\ddot {y}}={\frac {d^{2}y}{dt^{2}}}}"> </noscript><span class="lazy-image-placeholder" style="width: 14.042ex;height: 6.009ex;vertical-align: -2.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/435c2e695f8ab8be3077ba58f619789b8c546aa7" data-alt="{\displaystyle a_{y}={\ddot {y}}={\frac {d^{2}y}{dt^{2}}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>diperoleh</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{x}=-\omega ^{2}R\cos(\omega t+\phi _{x})\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> = </mo> <mo> − </mo> <msup> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> R </mi> <mi> cos </mi> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{x}=-\omega ^{2}R\cos(\omega t+\phi _{x})\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/298f01565d74537c13f072bbbdcca41f35db3bc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.166ex; width:24.344ex; height:3.176ex;" alt="{\displaystyle a_{x}=-\omega ^{2}R\cos(\omega t+\phi _{x})\!}"> </noscript><span class="lazy-image-placeholder" style="width: 24.344ex;height: 3.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/298f01565d74537c13f072bbbdcca41f35db3bc0" data-alt="{\displaystyle a_{x}=-\omega ^{2}R\cos(\omega t+\phi _{x})\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{y}=-\omega ^{2}R\sin(\omega t+\phi _{x})\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo> = </mo> <mo> − </mo> <msup> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> R </mi> <mi> sin </mi> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{y}=-\omega ^{2}R\sin(\omega t+\phi _{x})\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6493ada74808cf0ecb2b01e4b14dfe6f93269ff4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.166ex; width:23.965ex; height:3.343ex;" alt="{\displaystyle a_{y}=-\omega ^{2}R\sin(\omega t+\phi _{x})\!}"> </noscript><span class="lazy-image-placeholder" style="width: 23.965ex;height: 3.343ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6493ada74808cf0ecb2b01e4b14dfe6f93269ff4" data-alt="{\displaystyle a_{y}=-\omega ^{2}R\sin(\omega t+\phi _{x})\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>sehingga</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{T}={\sqrt {(-\omega )^{4}R^{2}\cos ^{2}(\omega t+\phi _{x})+\omega ^{4}R^{2}\sin ^{2}(\omega t+\phi _{x})}}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false"> ( </mo> <mo> − </mo> <mi> ω </mi> <msup> <mo stretchy="false"> ) </mo> <mrow class="MJX-TeXAtom-ORD"> <mn> 4 </mn> </mrow> </msup> <msup> <mi> R </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <msup> <mi> cos </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> + </mo> <msup> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 4 </mn> </mrow> </msup> <msup> <mi> R </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <msup> <mi> sin </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> </msqrt> </mrow> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{T}={\sqrt {(-\omega )^{4}R^{2}\cos ^{2}(\omega t+\phi _{x})+\omega ^{4}R^{2}\sin ^{2}(\omega t+\phi _{x})}}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b5fa7aa897784980393d2658362f785d5a9f33c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; margin-right: -0.387ex; width:52.971ex; height:4.843ex;" alt="{\displaystyle a_{T}={\sqrt {(-\omega )^{4}R^{2}\cos ^{2}(\omega t+\phi _{x})+\omega ^{4}R^{2}\sin ^{2}(\omega t+\phi _{x})}}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 52.971ex;height: 4.843ex;vertical-align: -1.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b5fa7aa897784980393d2658362f785d5a9f33c" data-alt="{\displaystyle a_{T}={\sqrt {(-\omega )^{4}R^{2}\cos ^{2}(\omega t+\phi _{x})+\omega ^{4}R^{2}\sin ^{2}(\omega t+\phi _{x})}}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{T}=\omega ^{2}R{\sqrt {\cos ^{2}(\omega t+\phi _{x})+\sin ^{2}(\omega t+\phi _{x})}}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo> = </mo> <msup> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> R </mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi> cos </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> + </mo> <msup> <mi> sin </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> ⁡ </mo> <mo stretchy="false"> ( </mo> <mi> ω </mi> <mi> t </mi> <mo> + </mo> <msub> <mi> ϕ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> </msqrt> </mrow> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{T}=\omega ^{2}R{\sqrt {\cos ^{2}(\omega t+\phi _{x})+\sin ^{2}(\omega t+\phi _{x})}}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b804fa49cb557a7346edb146f409c0020e5b85a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; margin-right: -0.387ex; width:42.207ex; height:4.843ex;" alt="{\displaystyle a_{T}=\omega ^{2}R{\sqrt {\cos ^{2}(\omega t+\phi _{x})+\sin ^{2}(\omega t+\phi _{x})}}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 42.207ex;height: 4.843ex;vertical-align: -1.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b804fa49cb557a7346edb146f409c0020e5b85a" data-alt="{\displaystyle a_{T}=\omega ^{2}R{\sqrt {\cos ^{2}(\omega t+\phi _{x})+\sin ^{2}(\omega t+\phi _{x})}}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{T}=\omega ^{2}R\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo> = </mo> <msup> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> R </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{T}=\omega ^{2}R\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d92a5fb1e653b3f64b96c0a9c377fe857f0bc8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.378ex; width:9.972ex; height:3.009ex;" alt="{\displaystyle a_{T}=\omega ^{2}R\!}"> </noscript><span class="lazy-image-placeholder" style="width: 9.972ex;height: 3.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d92a5fb1e653b3f64b96c0a9c377fe857f0bc8f" data-alt="{\displaystyle a_{T}=\omega ^{2}R\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <div class="mw-heading mw-heading3"> <h3 id="Kecepatan_sudut_tidak_tetap">Kecepatan sudut tidak tetap</h3><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=11&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Kecepatan sudut tidak tetap" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <p>Persamaan parametric dapat pula digunakan apabila gerak melingkar merupakan GMBB, atau bukan lagi GMB dengan terdapatnya kecepatan sudut yang berubah beraturan (atau adanya percepatan sudut). Langkah-langkah yang sama dapat dilakukan, akan tetapi perlu diingat bahwa</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega \rightarrow \omega (t)=\int \alpha dt=\omega _{0}+\alpha t\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω </mi> <mo stretchy="false"> → </mo> <mi> ω </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <mo> ∫ </mo> <mi> α </mi> <mi> d </mi> <mi> t </mi> <mo> = </mo> <msub> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> + </mo> <mi> α </mi> <mi> t </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega \rightarrow \omega (t)=\int \alpha dt=\omega _{0}+\alpha t\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/059b1ca665dc1f30b8587217aa9e0f731b63de6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-right: -0.315ex; width:29.071ex; height:5.676ex;" alt="{\displaystyle \omega \rightarrow \omega (t)=\int \alpha dt=\omega _{0}+\alpha t\!}"> </noscript><span class="lazy-image-placeholder" style="width: 29.071ex;height: 5.676ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/059b1ca665dc1f30b8587217aa9e0f731b63de6f" data-alt="{\displaystyle \omega \rightarrow \omega (t)=\int \alpha dt=\omega _{0}+\alpha t\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> α </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \alpha \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63fb046fc5e294f95686e8e90977c4280e5336b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.301ex; width:1.402ex; height:1.676ex;" alt="{\displaystyle \alpha \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.402ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63fb046fc5e294f95686e8e90977c4280e5336b8" data-alt="{\displaystyle \alpha \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> percepatan sudut dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{0}\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega _{0}\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4f1e115a64b8991b3acf59777082e469ad71a2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.5ex; height:2.009ex;" alt="{\displaystyle \omega _{0}\!}"> </noscript><span class="lazy-image-placeholder" style="width: 2.5ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4f1e115a64b8991b3acf59777082e469ad71a2e" data-alt="{\displaystyle \omega _{0}\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> kecepatan sudut mula-mula. Penurunan GMBB ini akan menjadi sedikit lebih rumit dibandingkan pada kasus GMB di atas.</p> <p>Persamaan parametrik di atas, dapat dituliskan dalam bentuk yang lebih umum, yaitu:</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x(t)=x_{c}+R\cos \theta \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> x </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> <mo> + </mo> <mi> R </mi> <mi> cos </mi> <mo> ⁡ </mo> <mi> θ </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle x(t)=x_{c}+R\cos \theta \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79f5ac7ff82324cdda4a5b6816833bb7dd14e80e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.371ex; width:18.915ex; height:2.843ex;" alt="{\displaystyle x(t)=x_{c}+R\cos \theta \!}"> </noscript><span class="lazy-image-placeholder" style="width: 18.915ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79f5ac7ff82324cdda4a5b6816833bb7dd14e80e" data-alt="{\displaystyle x(t)=x_{c}+R\cos \theta \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(t)=y_{c}+R\sin \theta \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> y </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> y </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> <mo> + </mo> <mi> R </mi> <mi> sin </mi> <mo> ⁡ </mo> <mi> θ </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle y(t)=y_{c}+R\sin \theta \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dc3c4310319c4726dbe741f983d17d062faa3e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.371ex; width:18.295ex; height:2.843ex;" alt="{\displaystyle y(t)=y_{c}+R\sin \theta \!}"> </noscript><span class="lazy-image-placeholder" style="width: 18.295ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dc3c4310319c4726dbe741f983d17d062faa3e3" data-alt="{\displaystyle y(t)=y_{c}+R\sin \theta \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>di mana <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta =\theta (t)\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> θ </mi> <mo> = </mo> <mi> θ </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \theta =\theta (t)\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09273d8c0a9fdbada7cc5d03414ed1ee41d2e983" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.166ex; width:7.708ex; height:2.843ex;" alt="{\displaystyle \theta =\theta (t)\!}"> </noscript><span class="lazy-image-placeholder" style="width: 7.708ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09273d8c0a9fdbada7cc5d03414ed1ee41d2e983" data-alt="{\displaystyle \theta =\theta (t)\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> adalah sudut yang dilampaui dalam suatu kurun waktu. Seperti telah disebutkan di atas mengenai hubungan antara <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> θ </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \theta \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4648910623b113399a15dc3065ab747ea127b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.371ex; width:1.074ex; height:2.176ex;" alt="{\displaystyle \theta \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.074ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4648910623b113399a15dc3065ab747ea127b5" data-alt="{\displaystyle \theta \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.345ex; width:1.404ex; height:1.676ex;" alt="{\displaystyle \omega \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.404ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62a7b63f7f5255194738f61169c1be0e95538d88" data-alt="{\displaystyle \omega \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> α </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \alpha \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63fb046fc5e294f95686e8e90977c4280e5336b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.301ex; width:1.402ex; height:1.676ex;" alt="{\displaystyle \alpha \!}"> </noscript><span class="lazy-image-placeholder" style="width: 1.402ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63fb046fc5e294f95686e8e90977c4280e5336b8" data-alt="{\displaystyle \alpha \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> melalui proses integrasi dan diferensiasi, maka dalam kasus GMBB hubungan-hubungan tersebut mutlak diperlukan.</p> <div class="mw-heading mw-heading4"> <h4 id="Kecepatan_sudut">Kecepatan sudut</h4><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=12&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Kecepatan sudut" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <p>Dengan menggunakan <a href="https://id-m-wikipedia-org.translate.goog/wiki/Aturan_rantai?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Aturan rantai">aturan rantai</a> dalam melakukan diferensiasi posisi dari persamaan parametrik terhadap waktu diperoleh</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{x}(t)=-R\sin \theta \ {\frac {d\theta }{dt}}=-\omega (t)R\sin \theta \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <mo> − </mo> <mi> R </mi> <mi> sin </mi> <mo> ⁡ </mo> <mi> θ </mi> <mtext>   </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mi> θ </mi> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <mo> = </mo> <mo> − </mo> <mi> ω </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mi> R </mi> <mi> sin </mi> <mo> ⁡ </mo> <mi> θ </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{x}(t)=-R\sin \theta \ {\frac {d\theta }{dt}}=-\omega (t)R\sin \theta \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d2e1882acbc8b3fa380156df1164ecf6e022a61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.371ex; width:35.532ex; height:5.509ex;" alt="{\displaystyle v_{x}(t)=-R\sin \theta \ {\frac {d\theta }{dt}}=-\omega (t)R\sin \theta \!}"> </noscript><span class="lazy-image-placeholder" style="width: 35.532ex;height: 5.509ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d2e1882acbc8b3fa380156df1164ecf6e022a61" data-alt="{\displaystyle v_{x}(t)=-R\sin \theta \ {\frac {d\theta }{dt}}=-\omega (t)R\sin \theta \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{y}(t)=R\cos \theta \ {\frac {d\theta }{dt}}=\omega (t)R\cos \theta \!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <mi> R </mi> <mi> cos </mi> <mo> ⁡ </mo> <mi> θ </mi> <mtext>   </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mi> θ </mi> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <mo> = </mo> <mi> ω </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mi> R </mi> <mi> cos </mi> <mo> ⁡ </mo> <mi> θ </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v_{y}(t)=R\cos \theta \ {\frac {d\theta }{dt}}=\omega (t)R\cos \theta \!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c72f3616d167346d2cb7a3bf02d9f728b6703c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.371ex; width:32.304ex; height:5.509ex;" alt="{\displaystyle v_{y}(t)=R\cos \theta \ {\frac {d\theta }{dt}}=\omega (t)R\cos \theta \!}"> </noscript><span class="lazy-image-placeholder" style="width: 32.304ex;height: 5.509ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c72f3616d167346d2cb7a3bf02d9f728b6703c6" data-alt="{\displaystyle v_{y}(t)=R\cos \theta \ {\frac {d\theta }{dt}}=\omega (t)R\cos \theta \!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>dengan</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d\theta }{dt}}=\omega (t)=\omega _{0}+\alpha \ t\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mi> θ </mi> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <mo> = </mo> <mi> ω </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> ω </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> + </mo> <mi> α </mi> <mtext>   </mtext> <mi> t </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\frac {d\theta }{dt}}=\omega (t)=\omega _{0}+\alpha \ t\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/635b2c72516d53f9ffe94da93fccee71050d4168" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-right: -0.315ex; width:21.61ex; height:5.509ex;" alt="{\displaystyle {\frac {d\theta }{dt}}=\omega (t)=\omega _{0}+\alpha \ t\!}"> </noscript><span class="lazy-image-placeholder" style="width: 21.61ex;height: 5.509ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/635b2c72516d53f9ffe94da93fccee71050d4168" data-alt="{\displaystyle {\frac {d\theta }{dt}}=\omega (t)=\omega _{0}+\alpha \ t\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>Dapat dibuktikan bahwa</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v(t)=v_{T}(t)={\sqrt {v_{x}^{2}(t)+v_{y}^{2}(t)}}=\omega (t)R\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> v </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> T </mi> </mrow> </msub> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> + </mo> <msubsup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </msqrt> </mrow> <mo> = </mo> <mi> ω </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mi> R </mi> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v(t)=v_{T}(t)={\sqrt {v_{x}^{2}(t)+v_{y}^{2}(t)}}=\omega (t)R\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/887f4d6361e69484fbb24add14ac6a470fa3c4dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.378ex; width:39.031ex; height:4.843ex;" alt="{\displaystyle v(t)=v_{T}(t)={\sqrt {v_{x}^{2}(t)+v_{y}^{2}(t)}}=\omega (t)R\!}"> </noscript><span class="lazy-image-placeholder" style="width: 39.031ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/887f4d6361e69484fbb24add14ac6a470fa3c4dd" data-alt="{\displaystyle v(t)=v_{T}(t)={\sqrt {v_{x}^{2}(t)+v_{y}^{2}(t)}}=\omega (t)R\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>sama dengan kasus pada GMB.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Gerak_berubah_beraturan">Gerak berubah beraturan</h2><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=13&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Gerak berubah beraturan" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <section class="mf-section-4 collapsible-block" id="mf-section-4"> <p>Gerak melingkar dapat dipandang sebagai gerak berubah beraturan. Bedakan dengan gerak lurus berubah beraturan (GLBB). Konsep kecepatan yang berubah kadang hanya dipahami dalam perubahan besarnya, dalam gerak melingkar beraturan (GMB) besarnya kecepatan adalah tetap, akan tetapi arahnya yang berubah dengan beraturan, bandingkan dengan GLBB yang arahnya tetap akan tetapi besarnya kecepatan yang berubah beraturan.</p> <table class="wikitable" style="text-align:center;"> <caption> Gerak berubah beraturan </caption> <tbody> <tr> <th width="80">Kecepatan</th> <th width="80">GLBB</th> <th width="80">GMB</th> </tr> <tr> <th>Besar</th> <td>berubah</td> <td>tetap</td> </tr> <tr> <th>Arah</th> <td>tetap</td> <td>berubah</td> </tr> </tbody> </table> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Lihat_pula">Lihat pula</h2><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=14&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Lihat pula" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <section class="mf-section-5 collapsible-block" id="mf-section-5"> <ul> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_jatuh_bebas?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gerak jatuh bebas">Gerak jatuh bebas</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_lurus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gerak lurus">Gerak lurus</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_peluru&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Gerak peluru (halaman belum tersedia)">Gerak peluru</a></li> <li><a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_vertikal&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Gerak vertikal (halaman belum tersedia)">Gerak vertikal</a></li> </ul> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Referensi">Referensi</h2><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=15&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Referensi" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <section class="mf-section-6 collapsible-block" id="mf-section-6"> <style data-mw-deduplicate="TemplateStyles:r18833634">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style> <div class="reflist"> <div class="mw-references-wrap"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-1">^</a></b></span> <span class="reference-text">Richard S. Westfall, <i>Circular Motion in Seventeenth-Century Mechanics</i>, <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=http://links.jstor.org/sici?sici%3D0021-1753%2528197206%252963%253A2%253C184%253ACMISM%253E2.0.CO%253B2-O">Isis, Vol. 63, No. 2. (Jun., 1972), pp. 184-189</a>.</span></li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="https://id-m-wikipedia-org.translate.goog/wiki/Gerak_melingkar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-2">^</a></b></span> <span class="reference-text"><i>Chapter 22 Parametric Equation,</i>, Department of Mathematics, University of Washington, <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=http://www.math.washington.edu/~m124/source/supps/week2/paraeqns1.pdf">Math 124 Materials (Autumn), ch 22, pp. 308</a> <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://web.archive.org/web/20060903203226/http://www.math.washington.edu/%257Em124/source/supps/week2/paraeqns1.pdf">Diarsipkan</a> 2006-09-03 di <a href="https://id-m-wikipedia-org.translate.goog/wiki/Wayback_Machine?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wayback Machine">Wayback Machine</a>..</span></li> </ol> </div> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Pranala_luar">Pranala luar</h2><span class="mw-editsection"> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=edit&section=16&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Pranala luar" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>sunting</span> </a> </span> </div> <section class="mf-section-7 collapsible-block" id="mf-section-7"> <ul> <li><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://web.archive.org/web/20100117190656/http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/embed05.htm">Circular Motion Lecture</a> – a video lecture on CM</li> </ul> <div class="navbox-styles"> <style data-mw-deduplicate="TemplateStyles:r23782733">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul 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position: absolute;"> </noscript> <div class="printfooter" data-nosnippet=""> Diperoleh dari "<a dir="ltr" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://id.wikipedia.org/w/index.php?title%3DGerak_melingkar%26oldid%3D23952655">https://id.wikipedia.org/w/index.php?title=Gerak_melingkar&oldid=23952655</a>" </div> </div> </div> <div class="post-content" id="page-secondary-actions"> </div> </main> <footer class="mw-footer minerva-footer" role="contentinfo"><a class="last-modified-bar" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gerak_melingkar&action=history&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB"> <div class="post-content last-modified-bar__content"><span class="minerva-icon minerva-icon-size-medium minerva-icon--modified-history"></span> <span class="last-modified-bar__text modified-enhancement" data-user-name="180.252.127.37" data-user-gender="unknown" data-timestamp="1691008861"> <span>Terakhir diubah pada 2 Agustus 2023, pukul 20.41</span> </span> <span class="minerva-icon minerva-icon-size-small minerva-icon--expand"></span> </div></a> <div class="post-content footer-content"> <div id="mw-data-after-content"> <div class="read-more-container"></div> </div> <div id="p-lang"> <h4>Bahasa</h4> <section> <ul id="p-variants" class="minerva-languages"></ul> <ul class="minerva-languages"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ar.wikipedia.org/wiki/%25D8%25AD%25D8%25B1%25D9%2583%25D8%25A9_%25D8%25AF%25D8%25A7%25D8%25A6%25D8%25B1%25D9%258A%25D8%25A9" title="حركة دائرية – Arab" lang="ar" hreflang="ar" data-title="حركة دائرية" data-language-autonym="العربية" data-language-local-name="Arab" class="interlanguage-link-target"><span>العربية</span></a></li> <li class="interlanguage-link interwiki-be mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://be.wikipedia.org/wiki/%25D0%2592%25D1%258F%25D1%2580%25D1%2587%25D0%25B0%25D0%25BB%25D1%258C%25D0%25BD%25D1%258B_%25D1%2580%25D1%2583%25D1%2585" title="Вярчальны рух – Belarusia" lang="be" hreflang="be" data-title="Вярчальны рух" data-language-autonym="Беларуская" data-language-local-name="Belarusia" class="interlanguage-link-target"><span>Беларуская</span></a></li> <li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://be-tarask.wikipedia.org/wiki/%25D0%2592%25D1%258F%25D1%2580%25D1%2587%25D0%25B0%25D0%25BB%25D1%258C%25D0%25BD%25D1%258B_%25D1%2580%25D1%2583%25D1%2585" title="Вярчальны рух – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Вярчальны рух" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li> <li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://bn.wikipedia.org/wiki/%25E0%25A6%25AC%25E0%25A7%2583%25E0%25A6%25A4%25E0%25A7%258D%25E0%25A6%25A4%25E0%25A7%2580%25E0%25A6%25AF%25E0%25A6%25BC_%25E0%25A6%2597%25E0%25A6%25A4%25E0%25A6%25BF" title="বৃত্তীয় গতি – Bengali" lang="bn" hreflang="bn" data-title="বৃত্তীয় গতি" data-language-autonym="বাংলা" data-language-local-name="Bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ca.wikipedia.org/wiki/Moviment_circular" title="Moviment circular – Katalan" lang="ca" hreflang="ca" data-title="Moviment circular" data-language-autonym="Català" data-language-local-name="Katalan" class="interlanguage-link-target"><span>Català</span></a></li> <li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://cs.wikipedia.org/wiki/Pohyb_po_kru%25C5%25BEnici" title="Pohyb po kružnici – Cheska" lang="cs" hreflang="cs" data-title="Pohyb po kružnici" data-language-autonym="Čeština" data-language-local-name="Cheska" class="interlanguage-link-target"><span>Čeština</span></a></li> <li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://cv.wikipedia.org/wiki/%25C3%2587%25D0%25B0%25D0%25B2%25D1%2580%25D0%25B0%25D1%2588%25D0%25BA%25D0%25B0%25D0%25BB%25D0%25BB%25D0%25B0_%25D0%25BA%25D1%2583%25C3%25A7%25C4%2583%25D0%25BC" title="Çаврашкалла куçăм – Chuvash" lang="cv" hreflang="cv" data-title="Çаврашкалла куçăм" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li> <li class="interlanguage-link interwiki-da mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://da.wikipedia.org/wiki/J%25C3%25A6vn_cirkelbev%25C3%25A6gelse" title="Jævn cirkelbevægelse – Dansk" lang="da" hreflang="da" data-title="Jævn cirkelbevægelse" data-language-autonym="Dansk" data-language-local-name="Dansk" class="interlanguage-link-target"><span>Dansk</span></a></li> <li class="interlanguage-link interwiki-de mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://de.wikipedia.org/wiki/Gleichf%25C3%25B6rmige_Kreisbewegung" title="Gleichförmige Kreisbewegung – Jerman" lang="de" hreflang="de" data-title="Gleichförmige Kreisbewegung" data-language-autonym="Deutsch" data-language-local-name="Jerman" class="interlanguage-link-target"><span>Deutsch</span></a></li> <li class="interlanguage-link interwiki-el mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://el.wikipedia.org/wiki/%25CE%259A%25CF%2585%25CE%25BA%25CE%25BB%25CE%25B9%25CE%25BA%25CE%25AE_%25CE%25BA%25CE%25AF%25CE%25BD%25CE%25B7%25CF%2583%25CE%25B7" title="Κυκλική κίνηση – Yunani" lang="el" hreflang="el" data-title="Κυκλική κίνηση" data-language-autonym="Ελληνικά" data-language-local-name="Yunani" class="interlanguage-link-target"><span>Ελληνικά</span></a></li> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://en.wikipedia.org/wiki/Circular_motion" title="Circular motion – Inggris" lang="en" hreflang="en" data-title="Circular motion" data-language-autonym="English" data-language-local-name="Inggris" class="interlanguage-link-target"><span>English</span></a></li> <li class="interlanguage-link interwiki-es mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://es.wikipedia.org/wiki/Movimiento_circular" title="Movimiento circular – Spanyol" lang="es" hreflang="es" data-title="Movimiento circular" data-language-autonym="Español" data-language-local-name="Spanyol" class="interlanguage-link-target"><span>Español</span></a></li> <li class="interlanguage-link interwiki-et mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://et.wikipedia.org/wiki/Ringliikumine" title="Ringliikumine – Esti" lang="et" hreflang="et" data-title="Ringliikumine" data-language-autonym="Eesti" data-language-local-name="Esti" class="interlanguage-link-target"><span>Eesti</span></a></li> <li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://eu.wikipedia.org/wiki/Higidura_zirkular" title="Higidura zirkular – Basque" lang="eu" hreflang="eu" data-title="Higidura zirkular" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li> <li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fa.wikipedia.org/wiki/%25D8%25AD%25D8%25B1%25DA%25A9%25D8%25AA_%25D8%25AF%25D8%25A7%25DB%258C%25D8%25B1%25D9%2587%25E2%2580%258C%25D8%25A7%25DB%258C" title="حرکت دایره‌ای – Persia" lang="fa" hreflang="fa" data-title="حرکت دایره‌ای" data-language-autonym="فارسی" data-language-local-name="Persia" class="interlanguage-link-target"><span>فارسی</span></a></li> <li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fi.wikipedia.org/wiki/Ympyr%25C3%25A4liike" title="Ympyräliike – Suomi" lang="fi" hreflang="fi" data-title="Ympyräliike" data-language-autonym="Suomi" data-language-local-name="Suomi" class="interlanguage-link-target"><span>Suomi</span></a></li> <li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://gl.wikipedia.org/wiki/Movemento_circular" title="Movemento circular – Galisia" lang="gl" hreflang="gl" data-title="Movemento circular" data-language-autonym="Galego" data-language-local-name="Galisia" class="interlanguage-link-target"><span>Galego</span></a></li> <li class="interlanguage-link interwiki-he mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://he.wikipedia.org/wiki/%25D7%25AA%25D7%25A0%25D7%2595%25D7%25A2%25D7%2594_%25D7%259E%25D7%25A2%25D7%2592%25D7%259C%25D7%2599%25D7%25AA" title="תנועה מעגלית – Ibrani" lang="he" hreflang="he" data-title="תנועה מעגלית" data-language-autonym="עברית" data-language-local-name="Ibrani" class="interlanguage-link-target"><span>עברית</span></a></li> <li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://hi.wikipedia.org/wiki/%25E0%25A4%25B5%25E0%25A5%2583%25E0%25A4%25A4%25E0%25A5%258D%25E0%25A4%25A4%25E0%25A5%2580%25E0%25A4%25AF_%25E0%25A4%2597%25E0%25A4%25A4%25E0%25A4%25BF" title="वृत्तीय गति – Hindi" lang="hi" hreflang="hi" data-title="वृत्तीय गति" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li> <li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://hr.wikipedia.org/wiki/Kru%25C5%25BEno_gibanje" title="Kružno gibanje – Kroasia" lang="hr" hreflang="hr" data-title="Kružno gibanje" data-language-autonym="Hrvatski" data-language-local-name="Kroasia" class="interlanguage-link-target"><span>Hrvatski</span></a></li> <li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://hu.wikipedia.org/wiki/K%25C3%25B6rmozg%25C3%25A1s" title="Körmozgás – Hungaria" lang="hu" hreflang="hu" data-title="Körmozgás" data-language-autonym="Magyar" data-language-local-name="Hungaria" class="interlanguage-link-target"><span>Magyar</span></a></li> <li class="interlanguage-link interwiki-is mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://is.wikipedia.org/wiki/Hringhreyfing" title="Hringhreyfing – Islandia" lang="is" hreflang="is" data-title="Hringhreyfing" data-language-autonym="Íslenska" data-language-local-name="Islandia" class="interlanguage-link-target"><span>Íslenska</span></a></li> <li class="interlanguage-link interwiki-it mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wikipedia.org/wiki/Moto_circolare" title="Moto circolare – Italia" lang="it" hreflang="it" data-title="Moto circolare" data-language-autonym="Italiano" data-language-local-name="Italia" class="interlanguage-link-target"><span>Italiano</span></a></li> <li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ja.wikipedia.org/wiki/%25E5%2586%2586%25E9%2581%258B%25E5%258B%2595" title="円運動 – Jepang" lang="ja" hreflang="ja" data-title="円運動" data-language-autonym="日本語" data-language-local-name="Jepang" class="interlanguage-link-target"><span>日本語</span></a></li> <li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://kn.wikipedia.org/wiki/%25E0%25B2%25B5%25E0%25B3%2583%25E0%25B2%25A4%25E0%25B3%258D%25E0%25B2%25A4%25E0%25B3%2580%25E0%25B2%25AF_%25E0%25B2%259A%25E0%25B2%25B2%25E0%25B2%25A8%25E0%25B3%2586" title="ವೃತ್ತೀಯ ಚಲನೆ – Kannada" lang="kn" hreflang="kn" data-title="ವೃತ್ತೀಯ ಚಲನೆ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li> <li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ko.wikipedia.org/wiki/%25EC%259B%2590%25EC%259A%25B4%25EB%258F%2599" title="원운동 – Korea" lang="ko" hreflang="ko" data-title="원운동" data-language-autonym="한국어" data-language-local-name="Korea" class="interlanguage-link-target"><span>한국어</span></a></li> <li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://lv.wikipedia.org/wiki/L%25C4%25ABkl%25C4%25ABnijas_kust%25C4%25ABba" title="Līklīnijas kustība – Latvi" lang="lv" hreflang="lv" data-title="Līklīnijas kustība" data-language-autonym="Latviešu" data-language-local-name="Latvi" class="interlanguage-link-target"><span>Latviešu</span></a></li> <li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://mk.wikipedia.org/wiki/%25D0%259A%25D1%2580%25D1%2583%25D0%25B6%25D0%25BD%25D0%25BE_%25D0%25B4%25D0%25B2%25D0%25B8%25D0%25B6%25D0%25B5%25D1%259A%25D0%25B5" title="Кружно движење – Makedonia" lang="mk" hreflang="mk" data-title="Кружно движење" data-language-autonym="Македонски" data-language-local-name="Makedonia" class="interlanguage-link-target"><span>Македонски</span></a></li> <li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ml.wikipedia.org/wiki/%25E0%25B4%25B5%25E0%25B5%25BC%25E0%25B4%25A4%25E0%25B5%258D%25E0%25B4%25A4%25E0%25B5%2581%25E0%25B4%25B3%25E0%25B4%259A%25E0%25B4%25B2%25E0%25B4%25A8%25E0%25B4%2582" title="വർത്തുളചലനം – Malayalam" lang="ml" hreflang="ml" data-title="വർത്തുളചലനം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li> <li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://pl.wikipedia.org/wiki/Ruch_jednostajny_po_okr%25C4%2599gu" title="Ruch jednostajny po okręgu – Polski" lang="pl" hreflang="pl" data-title="Ruch jednostajny po okręgu" data-language-autonym="Polski" data-language-local-name="Polski" class="interlanguage-link-target"><span>Polski</span></a></li> <li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://pt.wikipedia.org/wiki/Movimento_circular" title="Movimento circular – Portugis" lang="pt" hreflang="pt" data-title="Movimento circular" data-language-autonym="Português" data-language-local-name="Portugis" class="interlanguage-link-target"><span>Português</span></a></li> <li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ru.wikipedia.org/wiki/%25D0%259A%25D1%2580%25D1%2583%25D0%25B3%25D0%25BE%25D0%25B2%25D0%25BE%25D0%25B5_%25D0%25B4%25D0%25B2%25D0%25B8%25D0%25B6%25D0%25B5%25D0%25BD%25D0%25B8%25D0%25B5" title="Круговое движение – Rusia" lang="ru" hreflang="ru" data-title="Круговое движение" data-language-autonym="Русский" data-language-local-name="Rusia" class="interlanguage-link-target"><span>Русский</span></a></li> <li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sc.wikipedia.org/wiki/Movimentu_in_caminu_chirculare" title="Movimentu in caminu chirculare – Sardinia" lang="sc" hreflang="sc" data-title="Movimentu in caminu chirculare" data-language-autonym="Sardu" data-language-local-name="Sardinia" class="interlanguage-link-target"><span>Sardu</span></a></li> <li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sh.wikipedia.org/wiki/Kru%25C5%25BEno_gibanje" title="Kružno gibanje – Serbo-Kroasia" lang="sh" hreflang="sh" data-title="Kružno gibanje" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Kroasia" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li> <li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sk.wikipedia.org/wiki/Pohyb_po_kru%25C5%25BEnici" title="Pohyb po kružnici – Slovak" lang="sk" hreflang="sk" data-title="Pohyb po kružnici" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li> <li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sl.wikipedia.org/wiki/Kro%25C5%25BEenje" title="Kroženje – Sloven" lang="sl" hreflang="sl" data-title="Kroženje" data-language-autonym="Slovenščina" data-language-local-name="Sloven" class="interlanguage-link-target"><span>Slovenščina</span></a></li> <li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sq.wikipedia.org/wiki/L%25C3%25ABvizja_rrethore" title="Lëvizja rrethore – Albania" lang="sq" hreflang="sq" data-title="Lëvizja rrethore" data-language-autonym="Shqip" data-language-local-name="Albania" class="interlanguage-link-target"><span>Shqip</span></a></li> <li class="interlanguage-link interwiki-su mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://su.wikipedia.org/wiki/Gerak_muter" title="Gerak muter – Sunda" lang="su" hreflang="su" data-title="Gerak muter" data-language-autonym="Sunda" data-language-local-name="Sunda" class="interlanguage-link-target"><span>Sunda</span></a></li> <li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://tr.wikipedia.org/wiki/Dairesel_hareket" title="Dairesel hareket – Turki" lang="tr" hreflang="tr" data-title="Dairesel hareket" data-language-autonym="Türkçe" data-language-local-name="Turki" class="interlanguage-link-target"><span>Türkçe</span></a></li> <li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://uk.wikipedia.org/wiki/%25D0%259A%25D0%25BE%25D0%25BB%25D0%25BE%25D0%25B2%25D0%25B8%25D0%25B9_%25D1%2580%25D1%2583%25D1%2585" title="Коловий рух – Ukraina" lang="uk" hreflang="uk" data-title="Коловий рух" data-language-autonym="Українська" data-language-local-name="Ukraina" class="interlanguage-link-target"><span>Українська</span></a></li> <li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ur.wikipedia.org/wiki/%25DA%25AF%25D8%25B1%25D8%25AF%25D8%25B4%25DB%258C_%25D8%25AD%25D8%25B1%25DA%25A9%25D8%25AA" title="گردشی حرکت – Urdu" lang="ur" hreflang="ur" data-title="گردشی حرکت" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li> <li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://uz.wikipedia.org/wiki/Aylanma_harakat_va_uning_dinamikasi" title="Aylanma harakat va uning dinamikasi – Uzbek" lang="uz" hreflang="uz" data-title="Aylanma harakat va uning dinamikasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li> <li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://vi.wikipedia.org/wiki/Chuy%25E1%25BB%2583n_%25C4%2591%25E1%25BB%2599ng_tr%25C3%25B2n" title="Chuyển động tròn – Vietnam" lang="vi" hreflang="vi" data-title="Chuyển động tròn" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnam" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li> <li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://wuu.wikipedia.org/wiki/%25E5%259C%2586%25E5%2591%25A8%25E8%25BF%2590%25E5%258A%25A8" title="圆周运动 – Wu Tionghoa" lang="wuu" hreflang="wuu" data-title="圆周运动" data-language-autonym="吴语" data-language-local-name="Wu Tionghoa" class="interlanguage-link-target"><span>吴语</span></a></li> <li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://zh.wikipedia.org/wiki/%25E5%259C%2593%25E5%2591%25A8%25E9%2581%258B%25E5%258B%2595" title="圓周運動 – Tionghoa" lang="zh" hreflang="zh" data-title="圓周運動" data-language-autonym="中文" data-language-local-name="Tionghoa" class="interlanguage-link-target"><span>中文</span></a></li> <li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://zh-yue.wikipedia.org/wiki/%25E5%259C%2593%25E5%2591%25A8%25E9%2581%258B%25E5%258B%2595" title="圓周運動 – Kanton" lang="yue" hreflang="yue" data-title="圓周運動" data-language-autonym="粵語" data-language-local-name="Kanton" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> </section> </div> <div class="minerva-footer-logo"> <img src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" alt="Wikipedia" width="120" height="18" style="width: 7.5em; height: 1.125em;"> </div> <ul id="footer-info" 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