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Question

Find the ratio of magnitude of angular momentum of a rolling disc about origin to that about the point P on the disc, as shown in the figure.
1089290_a2690b0921fa4122abcba89ec8c8e4d5.jpg

A
2:1
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B
1:1
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C
1:3
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D
4:3
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Solution

The correct option is A 2:1
Angular momentum about c is Iw but I=12MR2Ic=MR2w2
but angular momentum of c w.r.t O
is mVR
so Io=Ic+mVR=Ic+m(wR)R
Io=mR2w2+mR2w=32mR2w
angular momentary of c w.r.t P is
m(VcVp) separation
=mV2.R2=mVR4
Vp= velocity of P w.r.t O is VP=R2w
=V2
angular momentum w.r.t P will be Ip=Ic+mVR4
Ip=mR2w2+mR2w4
velocity of C w.r.t O is
Vc=V
velocity of C w.r.t P will be VCVP=VV2=V2
IoIp=21

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