Halaman
A. Gerak MelingkarBeraturanB. PercepatanSentripetalC. Aplikasi GerakMelingkarD. Gerak MelingkarBerubahBeraturanGerak Melingkar%0<9,36,39/,80743,>60<0>,7?9.?<
"092,;,:<,92B,929,4660<0>,7?9.?<>4/,6>0<;09>,7607?,<60>46,60<0>,7?9.?<-0<20<,6;,/,<07B,928074926,< 0<,6-09/,-09/,B,92749>,=,99B,-0<?;,74926,<,9/4=0-?>20<,68074926,<(0-?,3-09/,/46,>,6,9807,6?6,920<,68074926,<-0<,>?<,9546,749>,=,99B,-0<?;,74926,<,9/,9607,5?,9-09/,>0<=0-?>6:9=>,9 0<,68074926,<=0<492/45?8;,4/,7,86034/?;,9=03,<43,<4,9>,<,7,4920<,6;09>47<:/,=0;0/,B,92=0/,92-0<;?>,<20<,6,960<0>,7?9.?<80924>,<4749>,=,9<07B,92-0<-09>?674926,<,9=,8;,420<,6,9-09/,-09/,B,92<07,>41-0=,<B,4>?20<,6,9;7,90>;7,90>80924>,<4",>,3,<4807,7?4749>,=,99B,,>,?:<-4>9B,;,6,320<,68074926,<4>?/,6,33?-?92,9,9>,<,20<,67?<?=B,92>07,39/,;07,5,<4/,920<,68074926,< 46,9/,4924980920>,3?45,A,-,9,>,=;0<>,9B,,9;0<>,9B,,9>0<=0-?>;07,5,<4-,-494/092,9-,4669menganalisis besaran Fisika pada gerak melingkar dengan laju konstan.Setelah mempelajari bab ini, Anda harus mampu:menerapkan konsep dan prinsip dasar kinematika dan dinamika benda titik.Hasil yang harus Anda capai:Roller coaster, pada kecepatan tertentu di lintasan yang menghadapke tanah penumpangnya tidak terjatuh.Bab4Sumber: CD Image
70Mudah dan Aktif Belajar Fisika untuk Kelas XA. Gerak Melingkar Beraturan;,6,3B,92/48,6=?//092,920<,68074926,<-0<,>?<,92,<9/,808,3,849B,7,6?6,96024,>,9-0<46?>%0<3,>46,9%)
(0-?,3;,<>4607-0<20<,6;,/,749>,=,9=0;,95,92-?=?<74926,<,9B,92-0<5,<45,<4(,,>-0<,/,/4>4>46;,<>46078084746460.0;,>,9 08?/4,9;,<>4607-0<20<,634922,-0<,/,/4>4>46/092,960.0;,>,9 07,5?,9;,<>4607/4>4>46/,9/4>4>46=,8,-0=,<9B,>0>,;460.0;,>,99B,>4/,6=,8, ,7494/4=0-,-6,960.0;,>,980<?;,6,9-0=,<,9@06>:<%,/,%)
>0<743,>-,3A,,<,360.0;,>,9;,<>4607/4;:=4=4-0<-0/,/092,9,<,360.0;,>,9;,<>460760>46,-0<,/,/4;:=4=4 ,/4A,7,?;?9947,4
=,8,-0=,<9B,/092,9947,4>0>,;4,<,360.0;,>,9;,<>4607/4=0>4,;>4>46;,/,749>,=,99B,>4/,6=,8,1.Laju Linear(0-?,3;,<>4607B,92-0<20<,68074926,<=0;0<>4;,/,%)
80908;?3749>,=,9=0;,95,926074749274926,<,9/092,9607,5?,9>0>,;/,9A,6>?>08;?3+,6>?B,92/4;0<7?6,9;,<>4607?9>?680908;?3=,>?6,74;?>,<,9/4=0-?>;0<4:/0,>,?A,6>?;?>,</4-0<47,8-,92/,9-,9B,69B,;?>,<,9B,92/47,6?6,9;,<>4607/,7,8=,>?=06:9/4=0-?>1<06?09=4/4-0<47,8-,92 ?-?92,9,9>,<,;0<4:/0/,91<06?09=480809?34;0<=,8,,9 $,%% %( $")!#'&* ( )# $!& #)# )"#&$ *'$*'$ )!#,+ $%,#,$+! &Tes Kompetensi Awal
;,B,929/,60>,3?4>09>,9220<,68074926,< ;,6,3B,92/48,6=?//092,91<06?09=4;0<4:/0/,97,5?7490,< %,/,20<,68074926,</4609,7=,>?,9<;8,;,B,929/,60>,3?4>09>,92=,>?,9>0<=0-?>
%,/,20<,67?<?=/4609,7;0<.0;,>,9/,;?9;,/,20<,68074926,</4609,7;0<.0;,>,9=?/?>;,6,3;0<-0/,,9,9>,<,/?,4=>47,3>0<=0-?> (0-?>6,9-09/,-09/,/4=064>,<9/,B,9280<?;,6,9.:9>:320<,68074926,<Aktivitas Fisika 4.1 )*
E
*" $'&') !"('#)#) ( )*" (( ' !*)Gambar 4.2Gerak melingkar dari sebuahpartikel.vvBAROGerak MelingkarTujuan PercobaanMengamati keadaan benda yang bergerak melingkar.Alat-Alat Percobaan1.Kaleng cat bekas2.Tali secukupnya3.AirLangkah-Langkah Percobaan1.Isilah kaleng bekas cat dengan air sampai kaleng cat terisi setengah.2.Ikatlah tali pada pegangan kaleng tersebut.3.Putar kaleng cat yang berisi air dengan tali sebagai pengikatnya dan tangansebagai poros putaran, seperti diperlihatkan pada gambar.4.Amati keadaan air dalam kaleng cat. Mengapa air tidak tumpah? Ataumengapa air tumpah?Gambar 4.1Uraian sebuah vektorperpindahan.ABv1v2RROs
71Gerak Melingkar" *" $' &$ $ " $)($,!)* )#&* "# ()* &' % &') !" #$#&* (**) ((' $ $# ! $" *" $'$-" R
E ('$&) $) $ $ '!*$( ( $ &'(#$$-#$
E )'$ $
" *" $'#( &' %( ' ' " $)($# '!*$( .Arah kecepatan linear pada setiaptitik selalu menyinggung lingkarandan arahnya selalu berubah.IngatlahTokohJohannes Kepler lahir di Weil(dekat Stutgart), Jerman. Iaalumnus Universitas Tübingen danpernah bekerja di sekolahLutheran di Graz, Austria. Setelahitu, ia bergabung dengan sebuahasosiasi bersama seorangastronom terkenal, Tyco Brahe.Kemudian, Kepler menjadi asistenBrahe di Praha, Republik Ceko.Hasil karyanya adalah hukum gerakplanet, yang kemudian digunakanoleh Newton untuk merumuskanhukum gravitasinya. Salah satuhukum tersebut adalah orbitplanet berbentuk elips. Pada saatitu, para astronom percaya bahwaorbit sebuah planet berbentuklingkaran. Kepercayaan ini telahberlangsung selama 2.000 tahun.Namun, berdasarkan perhitunganKepler ketika melakukanobservasi terhadap penelitianyang dilakukan oleh Brahe untukorbit planet Mars, bentuk orbitnyatidak berbentuk lingkaranmelainkan berbentuk elips.Sumber:Jendela IPTEK, "Gerak dan Gaya"2.Kecepatan Sudut (Kecepatan Anguler)%0<3,>46,9608-,74%)
(0-?,3;,<>4607-0<20<,68074926,<-0<,>?<,9/092,9=?/?>>08;?3/,7,8=07,92A,6>?t 0<,6;,<>4607;,/,=07,92A,6>?B,92=,8,,6,980908;?3-0=,<=?/?>B,92=,8,=034922,;0<=,8,,960.0;,>,9=?/?>/,;,>/4>?74=60.0;,>,9=?/?>(' (**) )#&* ,!)* )#&* ,7,8A,6>? ==0-?,3-09/,B,92-0<20<,68074926,<-0<,>?<,9/,;,>807,6?6,9
6,7474926,<,9;09?3)09>?6,9;0<4:/0/,91<06?09=420<,6-09/,>0<=0-?>.A,6>? B,92 /4-?>?36,9 ==5?87,3 74926,<,9 ;09?3
<06?09=4/434>?9280922?9,6,9 )*%&
0= C ,/4;0<4:/09B,,/,7,3=/,91<06?09=4,/,7,3 C(0-?,3-,>?/446,>/092,9=0?>,=>,74608?/4,9/4;?>,<=034922,-0<20<,68074926,<-0<,>?<,9/092,95,<45,<474926,<,9 8,>?807,6?6,96,74;?>,<,9=0>4,;/0>469B,0<,;,6,37,5?7490,<-,>?>0<=0-?>.460>,3?4 8/,96,74*9>?6809234>?92;0<4:/0/42?9,6,9 )*%&
01f =
8 = 8= ,/47,5?7490,<-,>?>0<=0-?>,/,7,3 8=Contoh 4.2Contoh 4.1Johannes Kepler(1571–1630)
72Mudah dan Aktif Belajar Fisika untuk Kelas X 0>0<,92,960.0;,>,9=?/?><,/=;0<4:/0=*9>?6=,>?;?>,<,9,>,?=,>?;0<4:/0-0=,<=?/?>B,92/4>08;?3,/,7,32<,/4,9,>,? D092,9/08464,92<,/4,9 D<,/4,9
D
<,/4,9
D 0.0;,>,9=?/?>/,;,>/4>?74=/,7,8;?>,<,98094>-4,=,/4=0-?>
,<>49B,
,>,?/,7,8
,7,8809B070=,46,9=:,76,/,926,/,929/,80908?6,9;0<=0;=4B,926074<?84=,79B,;0920<>4,9/,<41<06?09=4=?/?><>41<06?09=4=?/?>/4=494-?6,9-,9B,69B,;?>,<,9B,92/4>08;?3=0>4,;=,>?,9A,6>?>0>,;4-0=,<60.0;,>,9=?/?>=0>4,;=,>?,9A,6>?!0-438?/,3546,9/,80743,>=,>?,99B,B,4>?<,/=3.Hubungan Laju Linear dan Kecepatan Sudut ?-?92,9,9>,<,7,5?7490,</,960.0;,>,9=?/?>,92?70</4;0<:703/092,980922,-?926,9 )*%&
0/,9 )*%&
0
=034922,/4;0<:703/,9,<460/?,;0<=,8,,9>0<=0-?>/4;0<:703
E
,7,8=,>?;0<4:/0;,<>460780908;?3=?/?>=0-0=,<092,9/08464,960.0;,>,9=?/?>9B,,/,7,3
E 0>0<,92,960.0;,>,97490,<8=60.0;,>,9=?/?><,/=5,<45,<48%0<3,>46,9 )*%&
0 ,<4;0<=,8,,9>0<=0-?>/,;,>/46,>,6,9-,3A,?9>?660.0;,>,9=?/?>>0<>09>?60.0;,>,97490,</4;092,<?34:7035,<,6>0<3,/,;;?=,>;?>,<,9%)
80<?;,6,9=608,=0-?,3;4<492,9B,92=0/,92-0<;?>,<(?8-?;?>,<9B,>0<70>,6/4>4>46;?=,>;4<492,9$%4<492,9>0<=0-?>=0/,92-0<;?>,</,92,960.0;,>,9=?/?>B,926:9=>,9<>49B,=0>4,;=07,92A,6>?B,92=,8,>4>46,>,?>4>4680908;?3=?/?>;?>,<,9B,92=,8,)4>46/,980<?;,6,9>4>46>4>46B,92>0<70>,6;,/,;4<492,9>0<=0-?>=0/08464,9=034922,$$092,96,>,7,49>4>4680847464749>,=,974926,<,9B,925,<45,<49B,70-43-0=,</,<4;,/,5,<45,<4749>,=,9>4>460=,<60.0;,>,97490,<=0-?,3>4>46;,/,;4<492,9B,92=0/,92-0<:>,=4/4;092,<?34:7035,<,6>4>46>0<=0-?>/,<4>4>46;?=,>,<4%)
/,;,>/4=48;?76,9-,3A,60.0;,>,97490,<>4>4670-43-0=,</,<4;,/,60.0;,>,97490,<>4>46(08,649/06,>=0-?,3>4>46/,<4;?=,>;?>,<,9=08,64960.4760.0;,>,97490,<9B,/,;?960.0;,>,9=?/?>>4>46=,8,/092,960.0;,>,9=?/?>>4>46Gambar 4.3Kecepatan linear dipengaruhi olehjarak benda terhadap pusat putaranpada kecepatan sudut tertentu.vA1B0B1BB1A1vA0A0Ot2 = t +tt1 = tInformasiuntuk AndaPenggunaan variabel kecepatansudut dan kecepatan linear diantaranya adalah mengenaihubungan roda-roda bergerigi.Roda-roda bergerigi dihubungkanuntuk mempercepat,memperlambat, atau membalikputaran roda. Di antaranya adalah1.Susunan seporos:1 = 2vv=rr12122.Susunan bersinggungan:v1 = v21r1 = 2r23.Susunan terhubung sabuk:v1 = v21r1 = 2r2Information for YouUses of angular and linear velocityvariable is about gear connection.Gears connected to quicken, toslowing down or returning. There is:1.One axis formation2.Contact formation3.Incircuit belt formation.1r22r112r2r112r2r1
73Gerak Melingkar(0-?,3-09/,-0<20<,68074926,</092,960.0;,>,9
<;8<:>,=4;0<8094> 4>?927,3, ;0<4:/0;?>,<9B,- 60.0;,>,9=?/?>. 7,5?7490,<546,5,<45,<4<:/,=0;0/, .8.
<;8
;?>,<,98094>
;?>,<,9=
C, %0<4:/0,/,7,360-,746,9/,<41<06?09=4
C =- 0.0;,>,9=?/?>/434>?92/092,980922?9,6,9 )*%&
0
2f2
C8<,/=. ,<45,<4 .8 8!,5?7490,</434>?9280922?9,6,9 )*%&
0 R8 81,68= ,/4;0<4:/0;?>,<,99B, =60.0;,>,9=?/?>9B,8<,/=/,97,5?7490,<9B,,/,7,3
8=
*9>?680924>,<4749>,=,974926,<,9=0-,9B,6 6,74;?>,<,9=0-?,3-09/,8080<7?6,9A,6>? 8094>0<,;,;0<4:/0/,91<06?09=420<,6,9-09/,>0<=0-?> (0-?,3<:/,>?<-49;08-,9264>74=><46808474642,<4=>092,3 8/,9-0<;?>,<;,/, <;80<,;,6,3, 1<06?09=49B,- ;0<4:/09B,. 60.0;,>,9=?/?>9B,/ 7,5?7490,<;,/,;49224<<:/, /?,</?=80924>,<4749>,=,98074926,</092,9809209/,<,4=0;0/,8:>:<B,92<,/4?=9B, 8/092,9607,5?,9 685,8 4>?9260.0;,>,9=?/?>=0;0/,8:>:<>0<=0-?>/,7,8<,/=
07,=6,9;0920<>4,960.0;,>,97490,</,960.0;,>,9=?/?> (0-?,3-,>?/446,>/092,9>,74608?/4,9/4;?>,<6,9 46,;,95,92>,74
80>0</,9A,6>?B,92/4-?>?36,9?9>?6807,6?6,9=,>?;?>,<,9,/,7,3
=06:9-0<,;,6,360.0;,>,97490,<-,>?>0<=0-?> )"#&$ $%,#,$+! &Tes Kompetensi Subbab AB.Percepatan Sentripetal(0-?,3-09/,B,92807,6?6,920<,68074926,<-0<,>?<,980847464;0<.0;,>,9B,92,<,39B,809?5?>4>46;?=,>74926,<,9%0<.0;,>,9494/4=0-?>;0<.0;,>,9=09><4;0>,7%,/,20<,67?<?=-0<,>?<,9,<,360.0;,>,9-09/,>0>,;=034922,@06>:<60.0;,>,99B,5?2,>0>,;%,/,20<,68074926,<-0<,>?<,9;0<.0;,>,9B,92/4847464-0<1?92=48092?-,3,<,320<,6/,<420<,67?<?=8095,/420<,68074926,<-0<,>?<,9$703=0-,-4>?;0<.0;,>,9;,/,20<,68074926,<=07,7?809?5?60;?=,>B,92/4=0-?>;0<.0;,>,9=09><4;0>,7,>,?;0<.0;,>,9<,/4,7/,9/4-0<47,8-,92%,/,20<,68074926,<,<,360.0;,>,97490,<;,/,=0>4,;>4>46=07,7?809B4922?9274926,<,9/,9,<,39B,=07,7?-0<?-,3%0<?-,3,9@06>:<60.0;,>,9494/4=0-,-6,9,/,9B,;0<.0;,>,9=09><4;0>,7%,/,%)
546,60.0;,>,9-09/,;,/,>4>46 /,9!-0<>?<?>>?<?>/,98,6,-0/,60.0;,>,9E(024>42,!"#=0-,92?9/092,9=024>42,$ !=034922,,6,9/4;0<:703;0<-,9/492,9-0<46?>Gambar 4.4Arah kecepatan linear padagerak melingkar.ORKLSv1–v1NMv2v = v2 – v1sv–v1Contoh 4.3Kata Kunci•laju linear•kecepatan sesaat
74Mudah dan Aktif Belajar Fisika untuk Kelas X!"!#ss(07,95?>9B,,6,9/4;0<:703;0<=,8,,9 ,>,?=034922,;0<.0;,>,9<,>,<,>,8095,/4 at*9>?6=07,92A,6>?t809/06,>49:7>4>46 3,8;4<-0<48;4>/092,9>4>46!=034922,809/06,>49:7/,;?9t>4/,6=,8,/092,9>,634922,>0>,;4808474643,<2,B,92/4=0-?>;0<.0;,>,9=0=,,>B,92-0=,<9B,/4>?74=6,9=0-,2,4-0<46?>748
0t748
0t$7036,<09,7480t8,6,;0<.0;,>,9=0=,,>/,;,>/4>?74=6,9=0-,2,4-0<46?>Percepatan pada gerak melingkarselalu menuju ke pusat lingkaran.Ingatlah2
E0=,<;0<.0;,>,9=09><4;0>,7;,/,20<,68074926,<-0<,>?<,9=07,7?>0>,;/4=0>4,;>4>46/,9,<,39B,=07,7?809?5?60;?=,>74926,<,9%0<.0;,>,9=09><4;0>,7494-0<-,9/4927?<?=/092,96?,/<,>607,5?,97490,<-09/,$7036,<09,607,5?,97490,<=0-,9/492/092,9607,5?,9,92?70<-0=,<;0<.0;,>,9=09><4;0>,75?2,80<?;,6,91?92=46?,/<,>>0<3,/,;607,5?,9,92?70<9B,Dapatkah suatu bendadipercepat jika kelajuannyakonstan?Tantanganuntuk Anda
E 46,;,/, )*%&
0
/4=?-=>4>?=46,960 )*%&
0
)*%&
0
/,;,>/4>?74=6,9=0-,2,4-0<46?>
2 $7036,<09,;0<=,8,,9>0<=0-?>/,;,>/4>?74==0-,2,4-0<46?> 0>0<,92,9-0=,<;0<.0;,>,9=09><4;0>,78=-0=,<60.0;,>,97490,<8=5,<45,<4749>,=,981<06?09=4 C
ETugas Anda 4.1Dua buah roda dihubungkan sepertipada gambar. Jari-jari roda pertama5 cm jari-jari roda kedua 10 cm.Berapakah kecepatan roda 2 jikakecepatan sudut roda pertamaadalah 200 rpm?12r2r1
75Gerak MelingkarKata Kunci•kecepatan sentripetal•kecepatan sesaatTes Kompetensi Subbab B
(0-?,364;,=,9249-0</4,80>0<
.8-0<;?>,<;,/,
<;80<,;,;0<.0;,>,9=09><4;0>,7B,92/4,7,84?5?92?5?9264;,= (0-?,3-,>?/446,>/092,9>,74B,92;,95,929B,
8,7,8 /0>46-,>?807,6?6,9
;?>,<,9 4>?927,3;0<.0;,>,9=09><4;0>,7-,>?>0<=0-?> (0-?,3;4<492,9/092,95,<45,<4.8/4;?>,</092,960.0;,>,9=?/?> <,/=)09>?6,9;0<.0;,>,9=09><4;0>,7=0-?,3>4>46-0<8,==, 2B,92-0<,/,/4;49224<;4<492,9>0<=0-?> )"#&$ $%,#,$+! &
(0-?,3-09/,-0<20<,68074926,</092,9;0<.0;,>,9=09><4;0>,7 8=09/,>0<=0-?>-0<20<,6.8/,<4;?=,>74926,<,9 46,5,<,6-09/,8095,/4 6,74=08?7,34>?927,3;0<.0;,>,9=09><4;0>,79B, (0-?,3-09/,-0<20<,68074926,<,7,8A,6>? =06:9-09/,>0<=0-?>>07,3807,6?6,9;?>,<,90<,;,6,35,<,6-09/,>0<=0-?>>0<3,/,;;?=,>74926,<,9546,;0<.0;,>,9=09><4;0>,79B,
8=C. Aplikasi Gerak Melingkar1.Gerak Melingkar pada Bidang Vertikal *$ $)( #$#& $-
$%"!'))'&)( *#" &'# $$-$ #$ *$!$&' $( & '!#" $ !'& $ +') !"$)'" $
!%'!%'$ !')"*$*'%0<3,>46,9%)
%,/,60<0>,7?9.?<?=,3,B,92/4-0<46,9>0<3,/,;60<0>,7?9.?</,<480=4990<246490>46=0-07?8749>,=,98074926,<3,<?=80923,=476,960.0;,>,984948?8B,92/,;,>809,3,9;09?8;,92=034922,>4/,65,>?360>46,60<0>,-0<,/,/4,>,=749>,=,90<-0/,/092,9649.4<<,6=,=,6:<,6:<,>4/,6807,6?6,920<,6=,>?74926,<,9;09?3>0>,;420<,68074926,<8,6=48?89B,3,9B,=0>092,374926,<,9608?/4,9-:7,6-,746=0;0<>4=0-?,3-,9/?74749>,=,9>0<-,A,39B,>0</,;,>=?,>?-,9B,92809/:<:926:<,6:<,,2,</,;,>=07,7?-0<,B?9/092,9=08;?<9,Gambar 4.5a.Kereta luncur (roller coaster)b.Swing boat (kora-kora)(b)(a)Sumber:CD Image(0-?,3;4<492,934>,8=0/,92-0<;?>,</092,960.0;,>,9=?/?> <;80<,;,6,3;0<.0;,>,9=0-?,3>4>46;?>43B,92-0<,/,.8/,<4;?=,>;4<492,9>0<=0-?>.Contoh 4.4460>,3?4 <;8.8F
E 8 <;8 ;?>,<,98094> ;?>,<,9= ;?>,<,9= ,/41<06?09=4;?>,<,9;4<492,9>0<=0-?>,/,7,3 C5,<45,<4F
E 8%0<.0;,>,9=09><4;0>,7/,;,>/434>?92/092,9 )*%&
0 222 CF
E 8
8= ,/4;0<.0;,>,99B,,/,7,3
8=Kata Kunci•arah radial•gaya sentripetal
76Mudah dan Aktif Belajar Fisika untuk Kelas X2.Gerak Melingkar pada Arah Horizontal9/,8,=43492,>/092,9;0<.:-,,9B,92/47,6?6,9;,/,#+!-!+*!*!#
(0=?922?39B,20<,6,9B,928090<,;6,9;<49=4;B,92=,8,/,;,>9/,743,>;,/,=6,7,B,9270-43-0=,<84=,79B,;,/,;0<8,49,9:9>,92,9>492%0<3,>46,9%)
46,9/,=0/,92809?922,924;0<8,49,94949/,,6,980<,=,6,9=0:7,3:7,3=0/,92-0<20<,6/4;0<.0;,>8094922,76,9;:<:=;?>,<,9*9>?6809B0/0<3,9,6,9;0<=:,7,984=,79B,:9>,92,9>492>0<=0-?>=0/,92-0<20<,6-0<7,A,9,9,<,35,<?85,8/092,9607,5?,97490,<=0=,,>B,92>0>,;=0;0<>4/4;0<743,>6,9;,/,%)
9/,B,92=0/,92809,464:9>,92,9>49280923,/,;60,<,37?,<749>,=,98074926,<60.0;,>,9=0=,,>;,/,>4>464>?,/,7,3809B4922?9274926,<,9 46,>4/,6,/,B,92809,<469/,>,749/,,6,9-0<20<,6>0<-,928094922,76,9749>,=,9:9>,92,9>492(0-09,<9B,9/,=0/,92-0<20<,6/4;0<.0;,>809?5?60,<,3;?=,>74926,<,9Gambar 4.6Gerak penumpang pada permainanontang-anting.Tes Kompetensi Subbab C )"#&$ $%,#,$+! &
07,=6,97,38092,;,;09?8;,92
>4/,65,>?360>46,=0/,92-0<20<,6808-09>?674926,<,9 0>46,9,46;0<8,49,9:9>,92,9>4928092,;,9/,80<,=,=0,6,9,6,9>0<708;,</,9/4;0<.0;,>809?5?607?,<749>,=,9:9>,92,9>492 )?74=6,97,3,;746,=420<,68074926,<7,499B,/4=064>,<9/,Gambar 4.8Sebuah titik berpindah dari Amenuju B.t = 012t = tBAD. Gerak Melingkar Berubah Beraturan8,>47,3=0-?,3;09>47;,/,<:/,=0;0/,"4=,79B,;09>47=0;0/,9/,=0/,92-0<;?>,<8?7,4/,<4;?>,<,98094>8095,/4
;?>,<,98094>,<>49B,;09>47<:/,>0<=0-?>8092,7,84;0<?-,3,960.0;,>,9=?/?>0=,<9B,;0<?-,3,960.0;,>,9=?/?>;,/,=0>4,;>4>46,/,7,3>0>,;(,8,/092,920<,67?<?=-0<?-,3-0<,>?<,9;0<.0;,>,9/4/01494=46,9=0-,2,4;0<-,9/492,9,9>,<,;0<?-,3,960.0;,>,9/,9=07,92A,6>?>0<5,/49B,;0<?-,3,9>0<=0-?>%0<.0;,>,9;0<?-,3,9 60.0;,>,9=07,92 A,6>?,7,820<,68074926,<-0<?-,3-0<,>?<,9;0<.0;,>,9=?/?>9B,6:9=>,9/,;,>/4>?74=3?-?92,9=0-,2,4-0<46?>,>,?00
E9/,60>,3?4-,3A,0t/,9E8,6,;0<=,8,,99B,8095,/40,>,?0
E
percepatan semuyang dirasakanpenumpangvasp%0<;49/,3,9B,92/47,6?6,9;,<>4607-0=,<9B,,/,7,321/,7,8Gambar 4.7Diagram vektor gerak penumpangSumber: Dokumentasi Penerbit
77Gerak Melingkar=07,92A,6>?t0<,<>4-0=,<60.0;,>,9=?/?><,>,<,>,,/,7,3t0=,<,980<?;,6,9-0=,<60.0;,>,9<,>,<,>, 0.0;,>,9<,>,<,>,/,;,>/4/01494=46,9=0-,2,4947,4>092,3/,<460.0;,>,9,A,7/,960.0;,>,9,634<092,9/08464,9;0<=,8,,9/,;,>/4>?74=6,9=0-,2,4-0<46?>0(),>,?/,;,>/4>?74=6,95?2,/,7,8-09>?6-0<46?>0()092,9808,=?66,9;0<=,8,,9 0,6,9/4;0<:703 00()202 0
E
092,9/08464,9 )*%&
08095,/4 00 00 0>0<,92,9-0=,<=?/?>B,92/4>08;?3<,/060.0;,>,9=?/?>,A,7<,/=;0<.0;,>,9=?/?><,/=A,6>?= 46,9/,;0<3,>46,9;,/,20<,67?<?=-0<?-,3-0<,>?<,9>0<9B,>,8084746460=,8,,93?-?92,98,>08,>4=/092,920<,68074926,<-0<?-,3-0<,>?<,9$7036,<09,4>?9/,/,;,>809B070=,46,9;0<=:,7,9B,92809B,926?>60.0;,>,9=?/?>;0<.0;,>,9=?/?>/,9-0=,<=?/?>B,92/4>08;?3/092,9;0<=:,7,9B,92=,8,/092,920<,67?<?=-0<,>?<,9
E
$
%0<-,9/492,9 0<,6"074926,<0<?-,30<,>?<,9/092,9 0<,6!?<?=0<?-,30<,>?<,9 )#)&*$*! ), )+,)& ) (+&'&*+& )# $!& #) ), )+,)& ), &, ,+'&*+&0t 200tt 22002( )(0-?,3<:/,247,80=49/40=07-0<;?>,< <;8<:>,=4;0<8094>608?/4,9/48,>46,9=034922,<:/,-0<;?>,</4;0<7,8-,>=,8;,4-0<309>4/,7,8A,6>?
=06:9 46,;0<.0;,>,9=?/?>6:9=>,9-0<,;,6,74<:/,-0<;?>,<=0-07?8-0<309>4Contoh 4.5
78Mudah dan Aktif Belajar Fisika untuk Kelas X
(0-?,3>4>468,>0<4-0<20<,68074926,<-0<?-,3-0<,>?<,9/092,960.0;,>,9=?/?>,A,7 <,/=(0>07,3-0<20<,6=>4>468,>0<4>0<=0-?>-0<309>4)09>?6,97,3, ;0<.0;,>,9B,92/4,7,84>4>468,>0<4- -0=,<=?/?>B,92/4>08;?3 (0-?,38:>:<74=><46/,<460,/,,9/4,8-0<20<,6<:>,=4/092,960.0;,>,9=?/?>6:9=>,9=0-0=,<<,/==07,8,= 08?/4,98:>:<74=><46/4309>46,9/092,9;0<7,8-,>,96:9=>,9/,7,8
;?>,<,9)09>?6,97,3, ;0<?-,3,9=?/?>8:>:<74=><46- A,6>?B,92/4;0<7?6,9=0-07?88:>:<-0<309>4 (0-?,380=498080<7?6,9A,6>?=?9>?6-0<?-,3/,<460.0;,>,9=?/?>
<;88095,/4 <;8, 0<,;,6,3;0<.0;,>,9=?/?>9B,- 0<,;,-,9B,6;?>,<,9B,92/47,6?6,9/,7,8A,6>?>0<=0-?>
(0-?,3<:/,-0<;?>,</,<460,/,,9/4,860
<;8<:>,=4;0<8094>/,7,8A,6>? = 4>?927,3, ;0<.0;,>,9=?/?><:/,- -,9B,6;?>,<,9B,92/4-?,><:/,. 6:8;:909;0<.0;,>,9>,9209=4,7/,9=09><4;0>,7/,<4=0-?,3>4>46B,92-0<5,<,6
.8/,<4;?=,><:/,60>46,<:/,-0<;?>,</092,960.0;,>,9=?/?>
<;8Tes Kompetensi Subbab D )"#&$ $%,#,$+! &.460>,3?4 0.0;,>,9=?/?>,A,70 <;8;?>,<,9=+,6>?=,8;,4-0<309>4
=%0<7,8-,>,9<:/,/4;0<:703/092,9;0<=,8,,9> E E ;?>,<,9=
=;?>,<,9= ?87,3;?>,<,9/434>?92/092,9 )*%&
0 t>
(12);?>,<,9
= E E ;?>,<,9%,/,-,7,;,9;,<,;08-,7,;8084<4926,9609/,<,,9/,9-,/,99B,60>46,807,7?4>46?92,9"092,;,/08464,9;,B,92>0<5,/4546,;08-,7,;4>?>4/,68084<4926,9-,/,99B,Mari Mencari Tahu,>,?
0.0;,>,9=?/?>/4/01494=46,9=0-,2,4-0<46?>0=,<=?/?> >08;?3 0.0;,>,9 =?/?> +,6>?>08;?3 %0<.0;,>,9=09><4;0>,7;,/,20<,68074926,<,<,39B,809?5?>4>46;?=,>74926,<,9Rangkuman
0<,6-09/,B,92749>,=,99B,-0<?;,74926,<,9/4=0-?>20<,68074926,< <06?09=4;,/,20<,68074926,</4/01494=46,9=0-,2,4-,9B,69B,;?>,<,9B,92/47,6?6,9;,<>4607/,7,8=0>4,;=,>?,9A,6>? %0<4:/0;,/,20<,68074926,</4/01494=46,9=0-,2,4A,6>?B,92/4;0<7?6,9;,<>4607?9>?680908;?3=,>?6,74;?>,<,9
?-?92,9,9>,<,1<06?09=4/,9;0<4:/0;,/,20<,68074926,</4>?74=6,9=0-,2,4-0<46?>
79Gerak MelingkarPeta Konsep.4<49B, 0.0;,>,9=?/?>9B,6:9=>,9.4<49B, 0<,6"074926,<0<?-,30<,>?<,9>0</4<4,>,=%0<.0;,>,9=?/?>9B,-0<?-,3=0.,<,6:9=>,9 )# $!& #).4<49B,!49>,=,920<,69B,-0<?;,74926,<,9 0<,6"074926,<0<,>?<,9Setelah mempelajari bab ini, tentunya Anda dapatmenyebutkan contoh-contoh benda yang bergerakmelingkar yang ada di lingkungan Anda. Dapatkah Andamenyebutkan manfaat lain? Dari bab ini, bagian manakahRefleksidari materi bab ini yang Anda pahami? Agar semuamateri pada bab ini Anda pahami, cobalah diskusikandengan teman Anda atau minta penjelasan kepadaguru.
4>,8,9;0<8,4,9,9-,9B,6/4>0<,;6,9;<49=4;20<,68074926,</4,9>,<,9B,,/,7,36:<,6:<,/,960<0>,7?9.?<;,/,,<,3@0<>46,7(07,494>?;0<8,49,9:9>,92,9>4925?2,8090<,;6,9;<49=4;20<,68074926,<;,/,,<,33:<4C:9>,7 ,7,820<,68074926,<-0<?-,3-0<,>?<,9;0<.0;,>,9=?/?>9B,6:9=>,9B,4>?
80Mudah dan Aktif Belajar Fisika untuk Kelas X
09/,/46,>,6,9-0<20<,68074926,<546,, 60.0;,>,99B,>0>,;- 749>,=,99B,-0<?;,74926,<,9. 749>,=,99B,-0<?;,2,<4=7?<?=/ 749>,=,99B,>,680909>?0 ;0<.0;,>,99B,>0>,; <,360.0;,>,97490,<;,/,-09/,B,92=0/,92-0<20<,68074926,<,/,7,3, 809?5?;?=,>74926,<,9- -0<,=,7/,<4;?=,>74926,<,9. 809B4922?92749>,=,9/,9>02,67?<?=5,<45,<474926,<,9/ 8095,?34;?=,>74926,<,90 -0<7,A,9,9/092,9,<,320<,6 ,9B,69B,;?>,<,9=0>4,;=06:9;,/,20<,68074926,</4=0-?>, ;0<4:/0- 1<06?09=4. 60.0;,>,9=?/?>/ ;0<.0;,>,9=?/?>0 ;,95,92749>,=,9
(0-?,3-09/,-0<20<,68074926,<=07,8, 8094>-09/,>0<=0-?>>07,3807,6?6,9 ;?>,<,9+,6>?B,92/4;0<7?6,9-09/,?9>?6807,6?6,9=,>?;?>,<,9,/,7,3,
=06:9- =06:9. =06:9/
=06:90 =06:9 %0<3,>46,92,8-,<-0<46?>%0<9B,>,,9B,92-09,</,<42,8-,<>0<=0-?>,/,7,3, 60.0;,>,97490,</470-43-0=,</,<4;,/,60.0;,>,97490,</4- 60.0;,>,97490,</470-43-0=,</,<4;,/,60.0;,>,97490,</4. 60.0;,>,97490,</4$70-43-0=,</,<4;,/,60.0;,>,97490,</4/,9/ 60.0;,>,9=?/?>/470-4360.47/,<4;,/,60.0;,>,9=?/?>/4/,9$0 60.0;,>,97490,</470-43-0=,</,<4;,/,60.0;,>,9=?/?>/4$/,9 !$! $ *$ *+,".&/& ($!& + (+ &# )"#&$ ( ,#,$+! & (0-?,3-09/,-0<20<,68074926,</092,960.0;,>,9 <;8%0<9B,>,,9B,92-09,<,/,7,3, 60.0;,>,9>0<=0-?>80<?;,6,960.0;,>,97490,<- 1<06?09=4;?>,<,99B,,/,7,3;?>,<,9=06:9. 1<06?09=4;?>,<,99B,,/,7,3
;?>,<,9=06:9/ ;0<4:/0;?>,<,99B,,/,7,3 =06:90 60.0;,>,9=0/?>9B,<:>,=4=06:9 )4>46>0<70>,6/4>0;4;4<492,9B,92=0/,92-0<;?>,</,;?9>4>46>0<70>,6/4>092,3>092,35,<45,<4;4<492,9>0<=0-?>%0<-,9/492,960.0;,>,97490,<>4>46/,9>4>46,/,7,3,
/ -
0 .
(0-?,3-09/,B,92807,6?6,920<,68074926,<-0<,>?<,980847464, 60.0;,>,97490,<>0>,;- ;0<.0;,>,9>0>,;. 60.0;,>,9=?/?>>0>,;/ ;0<.0;,>,9/092,9,<,38095,?34;?=,>0 -0=,<;0<.0;,>,99B,=0-,9/492/092,960.0;,>,99B, %0<.0;,>,9=09><4;0>,7;,/,-09/,B,92-0<20<,68074926,<-0<,>?<,9-0<1?92=4, 809,8-,360.0;,>,9-09/,- 808;0<>,3,96,9,<,360.0;,>,9. 8092?-,3,<,360.0;,>,9/ 808-0<46,92,B,>,8-,3,90 808;0<>,3,96,9607,5?,9-09/,
,<?8=0-?,3=0;0/,8:>:<809?95?66,9,926,
<;8-0<,<>460.0;,>,9=?/?>;?>,<,980=498:>:<>0<=0-?>,/,7,3, <,/=/ <,/=-
<,/=0
<,/=. <,/=
46,=?,>?>4>46-0<20<,68074926,</092,9;0<4:/0>0>,;=0-0=,</0>46>4>46>0<=0-?>-0<20<,68074926,<, =,>?;?>,<,9=07,8,/0>46/092,97,5?>0>,;- ;?>,<,9=0>4,;/0>46/092,97,5?,92?70<-0<?-,3. ;?>,<,9=0>4,;/0>46/092,97,5?,92?70<>0>,;/ ;?>,<,9=0>4,;/0>46/092,97,5?,92?70<-0<?-,30 ;?>,<,9=0>4,;/0>46=0>07,34>?/4,8
,7,820<,68074926,<-0<,>?<,93?-?92,9,9>,<,/,9/49B,>,6,9/092,9;0<=,8,,9, /-0T.RORvBTes Kompetensi Bab 4
81Gerak Melingkar09/,B,928,==,9B, 2<,8/446,>6,9;,/,?5?92>,74/,9/43?-?926,9/092,9-0-,9807,7?4=0307,4
)4>46%/,9&-0<>?<?>>?<?>>0<70>,6;,/,?5?92/,9;0<>092,3,95,<45,<4=0-?,3<:/,B,92-0<;?>,<-0<,>?<,98,6,, 60.0;,>,9=?/?>/,960.0;,>,97490,<9B,=,8,- 60.0;,>,9=?/?>/,960.0;,>,97490,<9B,>4/,6=,8,. 60.0;,>,9=?/?>9B,=,8,>0>,;460.0;,>,97490,<9B,>4/,6=,8,/ 60.0;,>,9=?/?>9B,>4/,6=,8,>0>,;460.0;,>,97490,<9B,=,8,0 ;0<.0;,>,9=?/?>9B,>4/,6=,8,
%4<492,9-0</4,80>0< .8-0<;?>,</092,960.0;,>,9=?/?>
<,/= 46,=0-?,3>4>468,>0<4-0<,/,;,/,;49224<;4<492,9>0<=0-?>607,5?,97490,<9B,=0-0=,<, .8=-
.8=. .8=/ .8=0 .8=
0.0;,>,9,74<,9,4<B,92808?>,<649.4<,4<,/,7,3
.8= 46,2,<4=>092,3649.4< 860.0;,>,9=?/?>649.4<,/,7,3, <,/=-
<,/=.
<,/=/ <,/=0
<,/=
(?,>?>4>46807,6?6,920<,68074926,<-0<,>?<,9=034922,>4,;8094>808-?,> ;?>,<,9 46,5,<45,<4749>,=,99B,
.8;0<.0;,>,9=09><4;0>,79B,,/,7,3,
8=-
8=.
8=/
8=0
8=
%0<9B,>,,9B,92-09,<>09>,92;0<.0;,>,9=09><4;0>,7,/,7,3, ,<,39B,8095,?34;?=,>74926,<,9- ,<,39B,809?5?;?=,>74926,<,9. ,<,39B,>02,67?<?=5,<45,<4/ ,<,39B,-0<7,A,9,9,<,320<,60 ,<,39B,>02,67?<?=-4/,92749>,=,9
%0<9B,>,,9B,92-09,<>09>,92-0=,<;0<.0;,>,9=09><4;0>,7,/,7,3, -0<-,9/4927?<?=/092,96?,/<,>5,<45,<4;,/,60.0;,>,9>0>,;- -0<-,9/492>0<-,746/092,96?,/<,>5,<45,<4;,/,60.0;,>,9>0>,;. -0<-,9/4927?<?=/092,96?,/<,>60.0;,>,9546,5,<45,<49B,>0>,;/ >4/,6/4;092,<?34:7035,<45,<40 >4/,6/4;092,<?34:70360.0;,>,97490,<
09/,/46,>,6,9-0<20<,68074926,<-0<?-,3-0<,>?<,9546,, 60.0;,>,9=?/?>9B,>0>,;- 60.0;,>,9=?/?>9B,-0<?-,3=0.,<,-0<,>?<,9. ;0<.0;,>,99B,=,8,/092,99:7/ 60.0;,>,97490,<9B,>0>,;0 ;0<.0;,>,99B,>4/,6>0>,; (0-?,3<:/,=0;0/,=0/,92-0<;?>,<608?/4,9/4<08':/,>0<=0-?>,634<9B,-0<309>4=0>07,3
=06:9(07,8,A,6>?4>?<:/,=0;0/,>07,3-0<;?>,<=0-,9B,6 ;?>,<,9 46,;0<7,8-,>,9<:/,,/,7,3 ;?>,<,9=60.0;,>,9=?/?><:/,=0-07?8/47,6?6,9;0920<08,9,/,7,3, <;8-
<;8. <;8/
<;80 <;8 .$ ( )+&/& )!#,+!&! & &+ (+
(0-?,3-09/,-0<8,==,628092,7,8420<,6-0<,>?<,9/,7,8=?,>?749>,=,9-0<-09>?674926,<,9B,92-0<5,<45,<4 .8/092,960.0;,>,97490,< 8=)09>?6,9, ;0<4:/0;?>,<,9- ;0<.0;,>,9=09><4;0>,7 %0<3,>46,92,8-,<-0<46?>ABP-09,92 08?/4,9-09/,/4;?>,<809/,>,<=0;0<>4;,/,2,8-,<%,95,92>,74%,/,7,3 .8/,9?9>?6-0<;?>,< 6,74/4-?>?36,9A,6>?=)09>?6,9, ;0<4:/0;?>,<9B,- 60.0;,>,97490,<9B,. ;0<.0;,>,9=09><4;0>,7/,9,<,39B,/,9/ 2,B,=09><4;0>,7/,9,<,39B, 09/,B,928,==,9B,
2<,8807,6?6,920<,68074926,<-0<,>?<,9=0-,9B,6
;?>,<,9>4,;8094> ,<45,<474926,<,99B,
.8/,960.0;,>,99B, 8= 4>?927,3A,6>??9>?6=,>?6,74;?>,<
(0-?,38:-47807,5?;,/,=0-?,35,7,9809/,>,</092,9607,5?,9 685,8 46,5,<45,<474926,<,9-,98:-47,/,7,3 .8-0<,;,6,360.0;,>,9=?/?>;0<;?>,<,9-,9>0<=0-?> (0-?,364;,=,9249-0<;?>,< <;8
82Mudah dan Aktif Belajar Fisika untuk Kelas X, 0<,;,6,360.0;,>,9=?/?>>4>46B,92>0<70>,6;,/,-,7492-,7492- 0<,;,6,37,5?8,==,>4>46?5?92-,7492-,7492546,;,95,92-,7492-,7492,/,7,3 .8 (0-?,3<:/,-0<5,<45,<4
.8-0<;?>,<;,/,;:<:=9B,,7,8A,6>? /0>46<:/,>0<=0-?>/,;,>809.,;,460.0;,>,9 <;8/,<460,/,,9/4,8':/,>0<=0-?>/4;0<.0;,>-0<,>?<,9, 0<,;,6,3;0<.0;,>,9=?/?><:/,>0<=0-?>- 0<,;,6,3;0<.0;,>,9>,9209=4,7;,/,<:/, (0-?,36,><:7-0<5,<45,<4.8,7,8A,6>? /0>4660.0;,>,9=?/?>9B,-0<?-,3/,<4 ;?>,<,9=8095,/4 ;?>,<,9=, 0<,;,6,3;0<.0;,>,9=?/?>B,92/4,7,846,><:7- 0<,;,;?>,<,96,><:7>0<=0-?>-0<;?>,</,7,8A,6>? /0>46 (0-?,3-,98:-47-0<5,<45,<4 .8 46,8:-47/,<460,/,,9/4,8/,;,>/4;0<.0;,>-0<,>?<,9=034922,/,7,8A,6>?/0>4660.0;,>,99B,809.,;,4
8=-0<,;,6,3;0<.0;,>,9=?/?>-,9)07,3-0<;?>,<-0<,;,6,74-,9>0<=0-?> (0-?,3,7,>;0920<49280=49.?.4-0<;?>,<;,/,60.0;,>,9 ;?>,<,98094><;8/,9/4;0<7,8-,>-0<,>?<,9=034922,-0<;?>,<;,/, <;8%0<7,8-,>,9494/4.,;,4=0>07,3,7,>-0<;?>,< 6,74, 0<,;,6,3;0<.0;,>,9=?/?>80=49.?.4>0<=0-?>- 0<,;,6,3A,6>?B,92/4;0<7?6,9?9>?6809.,;,460.0;,>,9>0<=0-?>
(0-?,3-,>? 2/446,>;,/,?5?92>,74/,9/4;?>,<34922,80908;?374926,<,9/,>,<B,92-0<5,<45,<4
8/092,960.0;,>,9 ;?>,<,9=0>4,;/0>46)09>?6,9;0<.0;,>,9-,>?>0<=0-?>