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Question

# A disc of mass M and radius R is rolling with angular speed ω on a horizontal plane. The magnitude of angular momentum of the disc about the origin O is

A

12MR2ω

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B

MR2ω

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C

32MR2ω

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D

2MR2ω

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Solution

## The correct option is C 32MR2ω Let OC = R and let Vc be the velocity of the centre of mass of the disc. The linear momentum of the center of mass is Pc=Mvc. If Lc is angular momentum of the disc about C, then the angular momentum about origin O is L0=Lc+Rc×Pc ∴ Magnitude L0=lcω+Rc×Mvcsinθ=12MR2ω+MRcvc sin θ (∵Ic=12MR2)=12MR2ω+MR×Rω(∵Rcsin θ=R and vc=Rω)=32MR2ω

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