# Angular Momentum of a body after it loses mass

by SmoothCat
Tags: angular, body, loses, mass, momentum
 P: 2 Hey guys. If a body is spinning around the z - axis and an element of that body detaches on its own and flies off tangentially, does the rest of the remaining rotating body experience a change in angular velocity??? My thought is that the angular velocity of the remaining rotating body remains constant (same as body+elements' combined angular velocity at the start), just like velocity of a man holding a bowling ball on a moving skateboard remains constant before and after he drops it because both bodies keep the same momentum before and after the release, so its all good. Now for the rotating issue....... The body (without the element) has a certain angular momentum as it spins. The element itself has a moment of inertia mR^2 and also has its own angular momentum, which is exactly mvR or in terms of w, mwR^2. Now, after the element flies off on a tangent, it has the same angular momentum with respect to the axis of rotation as when it was attached, no matter how far it flies right, which is ---- m(r x v), which always works out to be of magnitude mvR, which is the same as before??? So does this mean that the body (without the element) would just keep rotating at the same angular velocity that the entire body + element had at the start of the problem because the angular momentum of the element never changes, so the same would need to be true for the remaining body as well. Please only send me a reply to this question if your willing to give me somewhat of a detailed response, because I'm really struggling with this idea...
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