This question follows from this post here.
Can linear momentum convert into angular monetum?
I would want to partly disagree that they cannot be transformed into one another.
Say for example we have a ball. We throw it such that it has a forward (top) spin (here "forward" is parallel to the ball's translational velocity, ie. its tangential velocity on top of the ball at any given point is in the same direction as its motion). Upon hitting the ground and bouncing, the ball will move faster in the direction it was moving due to the top spin. How did the ball gain extra translation motion? It should have come from somewhere.
To answer this question, I came up with 2 scenarios.
1. Some of the ball's angular momentum is transformed to linear momentum: When the ball hit the ground, the ball would experience a change in its spin and angular momentum. Since, momentum is not lost, it has to go somewhere – it transform to linear momentum (tangentially) – Whats perfect about this answer is that, the puzzle pieces of the ball's angular momentum being lost (spin slowed) and it suddenly gaining translational velocity, match up.
2. Obviously, with the first answer – doing the math, the domains don't add up…
Here's the second answer: What if they still do convert, but indirectly? This answer I have not thought of completely, as I could not find a proper medium or force for which they could convert through. In my mind, I think about it something like this: $$Ang \to R \to Translational$$ or vice-versa, where $R$ is the medium. In the ball scenario, we can express the change in translational momentum as $F\triangle t$, where the force would the medium. We know it has gained translational momentum because $v_{Intial} < v_{Final}$ with respect to the collision with the ground. Hence, the $F\triangle t > 0$, when considered with same direction of motion.
Question:
The answers are theoretical and display my ideas. My question is, why cannot angular momentum be converted to linear momentum (and vice-versa)(other than their dimensions/domain)? Even if the answer is no, how can one explain the ball scenario above?
Best Answer
You can't attack an interaction using conservation of momentum if you assume that one of the objects in the interaction has infinite mass and/or an infinitely distant center of mass. The angular momentum of the spinning ball goes into the angular momentum of the ball-Earth system, which can be closely approximated by treating the ball as a point mass with an initial angular velocity of 0 about an initially non-rotating sphere with a large but finite moment of inertia.