Consider a cylinder rolling on a horizontal plane. Its linear velocity is `v` and rotational angular velocity is `omega`. Find its angular momentum about point `P` on the ground as shown in Fig. What happens to this angular momentum if the cylinder is rotating in opposite direction but moving translationally in the same direction.

Explanation

In the given situation, cylinder tha both translational and rotational motion. We find its angular momentum about `P` by using the equation `vecL=vecL_(cm) +vecrxxmvecv`
The angular momentum of the clinder about its axis of rotation passing through its centre of mass is given by
`vecL_(C)=Iomega(-hatk)=(1/2mr^(2))omega(-hatk)`
And the angular momentum of this cyliner's translation motion about `P` is
`vecL=1/2mr^(2)omega+mvR(-hatk)`
If the cylinder rotates in anticlockwise directioiin and mvoes in the same direction, its total angular momentum wil now be written as
`vecL=1/2mr^(2)omega(hatk)+mvR(-hatk)=(1/2mr^(2)omega-mvR)(-hatk)`