k1
k2
k3 k4
M
M
*-*)-")3"-")3"45+"7"#"/8"/(1"-*/(4&1"4%"/,&2+","/-")1"%"#5,5-"4*)"/
-6B9252A<@@B5:?2D39@B:I@?D2=52?4F6BD:<2=C63E29 36?52H2?836B86B2<>6?8:<ED:86B2<A6=EBE>6> AE?H2:<@>A@?6?<@>A@?6?<646A2D2?H2?8 2 36C2B?H2D6D2AA2522B29352?36BE32936B2DEB2?
A2522B294
3 36C2B?H2D6D2AA2522B29452?36BE32936B2DEB2? A2522B293
4 36C2B?H2D6D2A32:<A2522B293>2EAE?A2522B294
5 36C2B?H236BE32936B2DEB2?32:<A2522B293
>2EAE?A2522B294
6 36C2B 52? 2B29?H2 D6BEC>6?6BEC 36BE329 D6B9252AG2<DE
)@C:C:C63E2936?525:?H2D2<2?56?82?A6BC2>22?
2JD *DOD+K>,6D6=2936?5236B86B2<
C6=2>2C6<@?<6=2;E2??H2252=29 2 5 > C 3 > C 6 > C 4 > C
!
)6B?H2D22? H2?8 D:52< 36?2B >6?86?2: 9E3E?82? 2?D2B2A6B46A2D2?D2?86?C:2=86B2<B@D2C:CE2DEA2BD:<6= 52?36C2B2?36C2B2?CE5ED?H2252=29
2 A6B46A2D2?D2?86?C:2=>6?E?;E<<2?A6BE3292? 36C2B<6=2;E2?=:?62B52B:A2BD:<6=
3 A6B46A2D2?D2?86?C:2=C6=2=E>6>:=:<:A2BD:<6=H2?8 36B86B2<>6=:?8<2B
4 A6B46A2D2? D2?86?C:2= >6>:=:<: A2BD:<6= H2?8 36B86B2<56?82?=2;E=:?62BD6D2A
5 A6B46A2D2? D2?86?C:2= C632?5:?8 56?82? A6B46A2D2?CE5ED52?;2B:;2B:
6 A6B46A2D2?D2?86?C:2=C6=2=E>6?82B29<6AEC2D =:?D2C2?>6=:?8<2B?H2
)@C:C:C63E2936?52H2?85:=6>A2B<2?F6BD:<2=<62D2C 5:?H2D2<2?56?82?A6BC2>22?4//>56?82?
/52=2>C6<@?$646A2D2?2G2=36?52252=29 2 > C 5 > C
3 > C 6 > C 4 > C
,63E2936?52H2?836B2D?H22>6=E?4EB<632G29 56?82?<646A2D2?D6D2AA252CE2DE3:52?8>:B:?8H2?8 <2C2B:52?8>:B:?8D6BC63ED>6>36?DE<CE5EDL D6B9252A9@B:I@?D2=$@67:C:6?86C6<2?2?D2B236?52 52?3:52?8D6BC63ED252=29
2
2 5
2 3
6
4
,63E2936?5236B>2CC2<85:5@B@?856?82?82H2 '2B29>6?52D2B$@67:C:6?86C6<2?<6D:<236?52 D6A2D2<2?36B86B2<252=29
2 5
3 6
4
#:<2A6B46A2D2?8B2F:D2C:5:A6B>E<22?E>:#52? ;2B:;2B:E>:>2<2A6B46A2D2?8B2F:D2C:5:CE2DED:D:< H2?836B;2B2<52B:A6B>E<22?E>:252=29 2
# 5 #
3
# 6 #
4 #
,63E29A682C56?82?D6D2A2?' >5:36B:3632?<8 52?5:D2B:<<62D2C56?82?A6B46A2D2?> C#:<2
#> C>2<2A6BD2>3292?A2?;2?8A682CD6BC63ED
252=29
2 > 5 > 3 > 6 > 4 >
,6@B2?8A6=2;2BH2?8>2CC2?H2<836B82?DE?8A252 E;E?8C63E29A682CC69:?882A682C36BD2>329A2?;2?8 4>6?82?56>:<:2?<@?CD2?D2A682C36B?:=2: 2 ' > 5 ' >
3 ' > 6 ' > 4 ' >
!
)682C5:CECE?C642B2C6B:52?A2B2=6=C6A6BD:82>32B 36B:<ED:?:
.;E?8A682C5:82?DE?8:3632?H2?8C2>236C2B#:<2 <@?CD2?D2A682C'''''A6B32?5:?82? A6B:@56CECE?2?C6B:52?A2B2=6=252=29
2 5
3 6
4
!
B27:<36B:<ED>6?E?;E<<2?86B2<2?C63E2936?52 36B>2CC2<8A2523:52?852D2BD2?A286C6<2?<2B6?2 A6?82BE982H2H2?836BE329E329
#:<2<646A2D2?36?52C22D.252=29> C>2<2 <646A2D2?36?52C22D.>252=29> C A6BE3292?6?6B8:<:?6D:<52B:.C2>A2:56?82?
.>252=29;@E=6
36C2BEC29252B:.C2>A2:56?82?.> 252=29;@E=6
)6B?H2D22?5:2D2CH2?836?2B252=29 2 52? 5 C2;2
3 52? 6 52?
4 52?
!
6?5236B>2CC2<85:=6>A2BF6BD:<2=<62D2C56?82? <646A2D2?2G2=> C6C2B?H26?6B8:A@D6?C:2=5: D:D:<D6BD:?88:H2?85:42A2:36?52252=29
2 # 5 #
3 # 6 #
4 #
,63E29 A682C H2?8 <@?CD2?D2?H2' 5:36B: 3632? 36B>2CC2)632?5:86D2B<2?56?82?2>A=:DE5@ ?6B8:A@D6?C:2=3632?:DEA252C22D<646A2D2??H2 <2=:<646A2D2?>2<C:>E>252=29
2 ' 5 '
3 ' 6 '
4 '
!
,63E2932=@<36B>2CC2<85:5@B@?852B:52C2BCE2DE 3:52?8>:B:?8H2?8A2?;2?8?H2>6D6B52?AE?42< 3:52?8>:B:?836B252>52B:D2?29#:<23:52?8>:B:?8 5:2?882A=:4:?52?A6B46A2D2?8B2F:D2C:E>:> C
EC292H2?892BEC5:=2<E<2?E?DE<>6?5@B@?832=@< 252=29
2 ;@E=6 5 ;@E=6 3 ;@E=6 6 ;@E=6 4 ;@E=6
,63E29 >@3:= 56?82? >2CC2 D@? 36B86B2< 52B: <62522? 5:2> ,6C22D <6>E5:2? <646A2D2??H2 >6?;25:> C6C2BEC292H2?85:=2<E<2?@=69>6C:? >@3:=D6BC63ED252=29
2 # 5 #
3 # 6 #
4 #
:2?D2B236?5236B86B2<36B:<ED:?:36?52H2?82<2? >6?82=2>:82H2A2=:?836C2B;:<2>6?E>3E<D6>3@< 9:?88236B96?D:252=29
2 36?5236B>2CC2<856?82?=2;E> C 3 36?5236B>2CC2<856?82?=2;E> C 4 36?5236B>2CC2<856?82?=2;E> C 5 36?5236B>2CC2<856?82?=2;E> C 6 36?5236B>2CC2<856?82?=2;E> C
)6=EBE56?82?>2CC28B2>52?<646A2D2?> C >6?86?2:52?>6?E>3E<C63E2932=@<56?82?>2CC2 <8H2?85:2>5:2D2C3:52?852D2BD2?A286C6<2? $646A2D2?A6=EBEC6D6=29>6?6>3EC32=@<252=29 > C$646A2D2?32=@<<2B6?2D6BD6>3ECA6=EBE 252=29
2 > C 5 > C 3 > C 6 > C 4 > C
@=236B>2CC2<8;2DE9D2?A2<646A2D2?2G2=<6 =2?D2: 52B: <6D:?88:2?$ >6D6B #:<2 A6B46A2D2? 8B2F:D2C:#52?<@67:C6?6=2CD:C:D2C3@=2D6B9252A=2?D2: 252=29>2<2A6B?H2D22?A6B?H2D22?D6?D2?83@=2 36B:<ED:?:36?2B'!0(%
2 36C2B <646A2D2? A2?DE=2? H2?8 A6BD2>2
#$
> C
3 36C2B <646A2D2? A2?DE=2? H2?8 <65E2
#$
> C
4 D:?88:>2<C:>2=A2?DE=2?A6BD2>2$> 5 D:?88:>2<C:>2=A2?DE=2?<65E24$>
6 <646A2D2?3@=2C22D>6?E>3E<=2?D2: #$> C ,63E29A6=EBE36B>2CC28B2>5:D6>32<<2?52B: C63E29C6?2A2?<62B29C63E2932=@<36B>2CC2<8 C69:?882A6=EBE36BC2B2?85:52=2>32=@<<2HED6BC63ED 2=@<36B2HE?52??2:<C6D:?88:4>52B:<62522? C6>E=2#:<2A6B46A2D2?8B2F:D2C:> C<646A2D2?
A6=EBEC6D6=29>6?86?2:32=@<252=29 2 > C 5 > C 3 > C 6 > C 4 > C
,63E293@=2<2CD:36B>2CC2<852=2><62522?5:2> <6>E5:2?5:AE<E=C69:?8823@=2>6=E?4EB56?82?=2;E > C52?A6>E<E=3@=2>6?H6?DE93@=2C6=2>2 C6<@?6C2B82H2A6>E<E=252=29
2 ' 5 '
3 ' 6 '
4 '
,63E2936?5236B@D2C:52B:<62522?5:2>C69:?882 52=2>G2<DEC6<@?>6>:=:<:<646A2D2?B25 C ,63E29D:D:<)36B252A25236?5252?36B;2B2<4> 52B:CE>3EB@D2C:?H2)6B46A2D2?D2?86?C:2=B2D2B2D2 H2?85:>:=:<:D:D:<)D6BC63ED252=29
F (N)
s (m) peluru
2 > C 5 > C
3 > C 6 > C
4 > C
)6B92D:<2? 82>32B 5: C2>A:?8 ,63E29 A:B:?82? 9@>@86?H2?8>6>:=:<:>2CC2)52?;2B:;2B:-5:AED2B A252C2=29C2DED:D:<5:82B:CC:?88E?8?H2&@>6?:?6BC:2 52B:A:B:?82?H2?85:AED2BD6BC63ED252=29
2
)- 5 )- 3
)- 6 )- 4 )-
,63E293@=2A6;2=36B>2CC2<852?36B;2B:;2B:4> @=2D6BC63ED>6?886=:?5:?85:A6B>E<22?;2=2?H2?8 <2C2B2<:32DC63E2982H25@B@?8'#:<23@=2 >6?886=:?5:?8 C6>AEB?2 >2<2 A6B46A2D2? H2?8 5:2=2>:3@=2A6;2=D6BC63ED252=29
2 > C 5 > C
3 > C 6 > C
4 > C
)6B92D:<2?C:CD6>A25282>32B36B:<ED 2H282H2H2?8 36<6B;2A25236?5252=2><62522?C6D:>32?8#:<2
# > C D682?82? 52? C:? >2C:?8>2C:?8
252=29 2 '52?
5 '52?
3 '52? 6 '52? 4 '52?
,63E29A:B:?82?36B36?DE< C:=:?56B9@>@86?36BAED2B A252 A@B@C?H2 56?82? <646A2D2? 2G2= B25 C :52?8 A:B:?82? C6;2;2B 3:52?89@B:I@?D2=&2CC2 A:B:?82?<852?;2B: ;2B:A:B:?82?>#:<2
5:2D2CA:B:?82?5:=6D2<<2?4:?4:?36B>2CC2<8 36B;2B:;2B:>52?AEC2D4:?4:?D6A2D5:2D2CAEC2D A:B:?82?>2<2<646A2D2?CE5EDA:B:?82?52?4:?4:? <6D:<236BAED2B252=29
2 B25 C 5 B25 C 3 B25 C 6 B25 C 4 B25 C
,63E2932<>2?5:36B36?DE<32=@<>6>:=:<:A2?;2?8 >=632B>52?D:?88:>2<>2?5:D6BC63ED 36B:C:=:D6B2:B%-
<8 >#:<2#> C
D6<2?2?9:5B@CD2D:<A25252C2B32<252=29
2 )2 5 )2
3 )2 6 )2
4 )2
,63E29A@>A29:5B@=:<>6>:=:<:5E2A6?89:C2AH2?8 36B;2B:;2B: >2C:?8>2C:?8 4> 52? 4> )252 A6?89:C2A<64:=5:<6B;2<2?82H2C636C2B' 2H2 H2?85:92C:=<2?A252A6?89:C2A36C2B252=29
2 '
3 '
4 '
5 '
6 '
6B:<ED4@?D@9A6?6B2A2?!E<E>6B?@E==:52=2> <69:5EA2?C692B:92B:'!0(%
2 82H22?8<2DA6C2G2DD6B32?8 3 <2B3EB2D@B>@3:=52?>@D@B 4 A6?H6>AB@D42:B2??H2>E< 5 F6?DEB:>6D6B
6 B6>9:5B@=:<
,63E29=@82>36B36?DE<3@=236B;2B:;2B:4>52? >2CC2;6?:C?H28 4>%@82>D6BC63ED;2DE93632C5:
52=2> 32< 36B:C: I2D 42:B H2?8 >6>:=:<: <@67:C:6? F:C<@C:D2C'C >#:<2>2CC2;6?:CI2D42:B8 4>52?
A6B46A2D2?8B2F:D2C:E>:> C>2<2<646A2D2?D6B
>:?2=3@=2=@82>252=29
2 > C 5 > C 3 > C 6 > C 4 > C
,63E29A:A2H2?8=EBEC>6>AE?H2:5E2A6?2>A2?8 56?82?=E2CA6B>E<22?>2C:?8>2C:?8>52?
>H2?85:=6D2<<2?C642B29@B:I@?D2=:B>6?82=:B
52B: A6?2>A2?8 36C2B <6 A6?2>A2?8 <64:= #:<2 <646A2D2?2BECA252A6?2>A2?836C2B> C<646A2D2? 2BEC2:BA252A6?2>A2?8<64:=252=29
2 > C 5 > C 3 > C 6 > C 4 > C
#:<2CE2DE82CH2?8>6>6?E9:!E<E>@H=65:;25:<2? C6D6?829?H2>2<2D6<2?2?>6?;25:5E2<2=:?H2!2= :?:5:C6323<2?<2B6?2
2 >@=6<E=>@=6<E=>6B2A2DC69:?882<646A2D2??H2 >6?;25:5E2<2=:
3 >@=6<E=>@=6<E=36B86D2B5E2<2=:=63:946A2D 4 >@=6<E=>@=6<E=36C2B?H2>6?;25:5E2<2=: 5 32?H2<?H2>@=6<E=>6?;25:5E2<2=:
6 6?6B8:<:?6D:<>@=6<E=>@=6<E=>6?;25:5E2<2=: #:<2<@?CD2?D2@=DI>2?'PO# <>2<2
6?6B8:<:?6D:<C63E292D@>82C96=:E>A252CE9EL 252=29
2 PO# 5 PO#
3 PO# 6 PO#
4 PO#
:52=2>BE2?836BF@=E>6%D6B52A2D>882C 36BD6<2?2?2D>#:<22D>' ><6=2;E2?
B2D2B2D2A2BD:<6=82CD6BC63ED252=29 2 > C 5 > C 3 > C 6 > C 4 > C
&2CC2C63E29>@=6<E=?:DB@86?252=29<2=:>2CC2 >@=6<E=9:5B@86?#:<2>@=6<E=?:DB@86?A252CE9E $>6>:=:<:=2;EB2D2B2D2H2?8C2>256?82?=2;E B2D2B2D2>@=6<E=9:5B@86?>2<252A2D5:A6B<:B2<2? CE9E9:5B@86?D6BC63ED252=29
sumbu putar piringan
r
30 N
4 kg
2 $ 5 $
3 $ 6 $
4 $
:<6D29E:82C!6C632?H2=>@=52?CE9E?H2L ?6B8:52=2>82C?H2252=29
2 ;@E=6 5 ;@E=6 3 ;@E=6 6 ;@E=6 4 ;@E=6
,63E29D23E?836B:C:%82C:562=A252CE9EL $6>E5:2?82CD6BC63ED5:A2?2C<2?C69:?882CE9E?H2 >6?;25:L#:<2D6<2?2?>E=2>E=282C252=29 P)252?F@=E>6D23E?8D6D2AD6<2?2?82CA252
D23E?8252=29
2 P)2 5 P)2
3 P)2 6 P)2
4 P)2
!2B8267:C:6?C:CE2DE>6C:?H2?836<6B;2A252B6C6BF@:B CE9EB6?529L52?CE9ED:?88:L252=29
2 5
3 6
4
,63E29=6>2B:6C36BCE9EOL=E:52H2?85:>2>A2D <2? 5: 52=2>?H2 >6?86>3E? A252 CE9E L $@67:C:6?52H28E?2=6>2B:6CD6BC63ED252=29
2 $ 5 $
3 $ 6 $
4 $
,63E29>6C:?2B?@B>6?88E?2<2?B6C6BF@:BCE9E D:?88:$52?>6>:=:<:67:C:6?C:82B67:C:6?C: ?2:< >6?;25: CE9E B6C6BF@:B D:?88: 92BEC 5:?2:<<2?C636C2B
2 $ 5 $
3 $ 6 $
4 $
,63E29>6C:?A6?5:?8:?BE2?82?>6>:=:<:52H2 G2DD#:<2CE9EBE2?82?L52?CE9EE52B2 L32?H2<?H2<2=@BH2?85:C6B2A>6C:?A6?5:?8:? C6=2>2>6?:D252=29
2 P# 5 P#
3 P# 6 P#
4 P#
"7"#-")1&24"/8""/#&2*,54%&/("/4&1"4
,63E29A2BD:<6=36B86B2<52B:A@C:C:2G2=*+, >6D6B56?82?<646A2D2?D6D2AH2?836C2B?H2> C #:<2=:?D2C2?A2BD:<6=>6=2=E:>>O>9:DE?8 =29F6<D@B<646A2D2?A2BD:<6=D6BC63ED
#:<2A6B46A2D2?8B2F:D2C:5:A6B>E<22?E>:> C
52?PO'> <8D6?DE<2?=29>2CC2
E>:H2?836B36?DE<3@=256?82?;2B:;2B:<> ,63E29A682C36B86D2B92B>@?:C56?82?2>A=:DE5@
4>!:DE?8=29C:>A2?82?86D2BC22D6?6B8:<:?6D:< 5E2<2=:6?6B8:A@D6?C:2=
,63E29A6=EBEH2?8>2CC2?H28B2>5:D6>32<<2? 52? >6?86?2: 32=@< <2HE 36B>2CC2 <8 H2?8 D6B=6D2<5:A6B>E<22?3:52?852D2B<2C2B56?82?
'
#:<2A6=EBE36BC2B2?85:52=2>32=@<H2?8 >6?82<:32D<2? 32=@< 36B86C6B C6;2E9 >6D6B D6?DE<2?=29 <646A2D2? A6=EBE C6C22D C636=E> >6?6>3EC32=@<8> C
!
E23E2936?52H2?8>6>:=:<:>2CC2))<8 36B86B2<C2=:?8>6?56<2D:C6A6BD:A25282>32B 36B:<ED
#:<2<65E236?5236BDE>3E<<2?=6?D:?8C6>AEB?2 D6?DE<2?=29<646A2D2?>2C:?8>2C:?836?52C6D6=29 36BDE>3E<<2?52?D6?DE<2?AE=22B29?H2
,63E2932D2?8),>2CC25:232:<2?A2?;2?8?H2 >)**++,-6?DE<2?>@>6?82H2H2?8 36<6B;2A25232D2?8;:<2
2 AEC2D>@>6?82H25:) 3 AEC2D>@>6?82H25:,
100
2 5
1 0 6 0
E B A
C F
=E:52:562=56?82?<646A2D2?> C5:52=2>A:A2 36B82B:CD6?8294>>2CE<<652=2>A:A236B82B:C D6?8294>-6?DE<2?=29<646A2D2?2=:B7=E:52A252 A:A2H2?836C2B
2=2>C63E29BE2?8D6BDEDEA36BF@=E>6=:D6BD6B52A2D >@=82C36BD6<2?2?)2#:<2A2BD:<6=82C>6>:=:<:
<6=2;E2?B2D2B2D2> CD6?DE<2?>2CC282C52? 6?6B8:<:?6D:<B2D2B2D282CD6BC63ED
2C@<C:86?36B25252=2>BE2?8D6BDEDEA36BCE9EL 52?D6<2?2?2D>C6BD2F@=E>6?H2%$6>E5:2? 82C@<C:86?D6BC63ED5:A2?2C<2?C2>A2:LC69:?882 D6<2?2??H2 ?2:< 2D> -6?DE<2? F@=E>6 82C C6<2B2?8
,E2DE82C52=2>C:=:?56BD6BDEDEA>6?82=2>:AB@C6C C6A6BD:A2528B27:<36B:<ED
-6?DE<2?EC292H2?85:=2<E<2?82CA252 2 AB@C6C
3 AB@C6C 4 AB@C6C 5 C6=EBE9AB@C6CD@D2=
m1 m2
v2 = 20 m/s v1 = 10 m/s
p (N/m2)
