A disk is undergoing pure rolling motion with speed v. The radius of the disk being R and mass M. Then the angular momentum of the disk about the
1)bottom most and
2)top most point
1) L(orbital) = m*v*r where v is the velocity of cm which is perpendicular to the given axis and r is the perpendicular distance between vector mv and and the axis.
2) L(spin) = Iw where I is the moment of inertia about the axis of rotation
The Attempt at a Solution
I got the answer in the first case-Since bottom most point is stationary in pure rolling I took L(orbital) as mvr and L(spin) as I*w=(MR^2/2)*w= mvr/2. adding both since both are in a clockwise sense- I get the answer L=1.5MVR which is correct.
In the second case however- the topmost point has velocity 2v and therefore v(cm) is relatively going to v to the left w.r.t to that point. since mv is in a clockwise sense, I took L(orbital) as mvr again and Iw remains unchanged giving the same answer which is incorrect, please let me know where I'm wrong