A bug sits on the edge of a disk as the disk rotates counterclockwise. Later, the bug starts to move in the direction of the disk's rotation. Does the disk's angular momentum increase, decrease, or stay the same?
stay the same. What ever angular momentum the bug gains, the disk loses. Newtons third law.
Wouldn't it be that the disk's momentum is decreasing, but that of the bug-disk system is the same (because the question is asking about the former)?
Yes.
The total angular momentum stays the same, but the bug pushes back on the disk to move forward on it.
To determine the change in angular momentum of the disk, we need to consider the angular momentum of both the disk and the bug.
The angular momentum of an object is given by the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Initially, when the bug is sitting on the edge of the disk, the angular momentum of the disk-bug system is the sum of the individual angular momenta. Let's call the angular momentum of the disk LD and the angular momentum of the bug LB.
At this point, the bug is stationary, so its angular velocity ω is zero. Therefore, its angular momentum LB would also be zero.
However, the disk is rotating counterclockwise, so it has some non-zero angular velocity ω and moment of inertia I. Hence, the angular momentum of the disk LD is non-zero.
So, initially, the total angular momentum of the system is the angular momentum of the disk-bug system, which is just LD.
Later, when the bug starts moving in the direction of the rotation, it will begin to acquire angular momentum. As the bug moves, its distance from the axis of rotation changes, increasing its moment of inertia. Consequently, the angular velocity ω of the bug also increases.
As a result, the angular momentum of the bug LB will become nonzero since both ω and I are non-zero.
Since the total angular momentum of the system is the sum of the angular momenta of the disk and the bug, it will increase due to the addition of the non-zero angular momentum of the bug. Therefore, the disk's angular momentum will increase when the bug starts to move in the direction of the rotation.