A man of mass m1 is standing on a disk with radius R and mass M at a distance r
The man starts walking around the disk with constant angular speed w1 and as a result the disk begins to rotate in the opposite direction with constant angular speed w2 (angular momentum is conserved). At the same time, the point mass m2 begins to move slowly towards the edge of the disk. The mass then falls off the edge of the disk.
The question is this: if the man were to stop walking after the point mass falls off of the disk, what direction will the disk rotate? Will it stop rotating, continue rotating in the same direction, or reverse directions?
I'm basically going between 2 thought processes with this problem, and I dont know which is right: 1) If the point mass os treated as part of the disk, then when it falls, the moment of inertia of the disk will be reduced. However, angular momentum is conserved, so the angular speed of the disk will increase as a result. This would then imply that if the man were to stop, then the disk would also stop. 2) As the disk slides away from the axis of rotation, the angular momentum of the system increases in the direction of rotation of the disk. After the disk falls off, the angular momentum stays at the elevated level, so that when the man stops, the disk continues to spin in the direction it was originally spinning.