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A sphere of mass M rolls without slippin...

A sphere of mass `M` rolls without slipping on a rough surface with centre of mass has constant speed `v_(0)`. If mass of the sphere is m and its radius be `R`, then find the angular momentum of the sphere about the point of contact.

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Since `vec(L)_(P) = vec(L)_(cm) + vec(r) xx vec(rho)_(cm) = I_(cm) vec(omega) + vec(R) xx m vec(v)_(cm)`
Since sphere is in pure rolling motion hence `omega = v_(0)//R`
`rArr" "vec(L) = ((2)/(5)MR^(2)) (v_(0))/(R) (-hat(k)) + Mv_(0) R (-hat(k))=(7)/(5) Mv_(0) R (-hat(k))`
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