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Question

# A disc of mass M and radius R is rolling without slipping with angular speed ω on a horizontal plane as shown in figure. The magnitude of angular momentum of the disc about the x−axis 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 For pure rolling, v=Rω where, v= linear velocity of COM of disc. ω= angular velocity of disc. ⇒Angular momentum about x−axis will include the angular momentum due to translation as well as angular momentum due to rotational motion. ∴→L=→LTrans+→LRot Angular momentum about x−axis is given by (L) ⇒L=MvCMR+ICMω ∵ICM=MR22 and vCM=Rω So, L=M(Rω)R+(MR22×ω) +ve sign taken since both angular momentums have a clockwise sense about x−axis. ∴L=32MR2ω

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