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Question

A uniform solid disc, is performing pure rolling on a fixed horizontal surface as shown in figure.

O, A and B are three points lying on y-axis where as C is top most point and D is bottom most point of the disc at the instant shown. Choose the correct option(s).

A
Angular momentum of disc with respect to C and D are same
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B
Magnitude of angular momentum of disc with respect to A (among O, A, B, C and D) is minimum
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C
Magnitude of angular momentum of disc with respect to B (among O, A, B, C and D) is minimum
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D
Angular momentum with respect to O and C are same
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Solution

The correct options are
A Angular momentum of disc with respect to C and D are same
B Magnitude of angular momentum of disc with respect to A (among O, A, B, C and D) is minimum
D Angular momentum with respect to O and C are same
LA=m(R×V)+IcomωLA=mVcmR2^k+mR22ω(^k)=0

LB=mR22ω(^k)

Since C point is lying on body and point D is Instataneous centre of rotation, therefore for both point we can use,
L=Iaboutthatpointω
Since, IC=ID=Icom+m(R)2=32mR2
LC=32mR2ω(^k) and
LD=32mR2ω(^k)

Now,
LO=mVcmR(^k)+mR22ω(^k)LO=32mR2ω(^k)
Therefore, angular momentum with respect to O and C are same. Also, magnitude of angular momentum of disc with respect to B (among O, A, B, C and D) is minimum

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