Why is angular momentum conserved?

In summary, the conversation discusses a problem from David Morin's Classical Mechanics and the solution provided in the manual. The question is raised about why Morin conserves angular momentum about a specific point, despite the torque from gravity due to the ball's weight. The statement in brackets explains that the torque is only relevant during the subsequent rising-up motion, but not during the instantaneous collision, as the collision time is too short for any significant change in angular momentum. This supports the argument that the torque from gravity does not affect the angular momentum during the collision.
  • #1
Abhishek11235
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So,this is problem from David Morin's Classical Mechanics(Screenshot 1). I solved the problem. Then I went to see the solution in manual hoping for out of box thinking. As in screenshot 2 is solution by Morin. My question is why he conserves angular momentum about the point (R-h) below C.M? There is torque due to its own weight. Actually I want to understand meaning of the statement he has written in bracket.

If texts is small here is what he has written:
"torque from gravity will be relevant during the subsequent rising-up motion. But during the instantaneous collision, L does not change."
Screenshot_2019-02-15-23-46-47.jpeg
Screenshot_2019-02-15-23-52-23.jpeg
 

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  • #2
You are looking at a collision that is being modeled as instantaneous. As long as this is a good approximation is appropriate, the time of the collision is too short for the torque to transfer any relevant angular momentum to the system.
 
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  • #3
The argument is that although there is a torque due to gravity while the ball is rotating about the corner, the time required for the ball to go over the corner is short enough so that the angular momentum does not change appreciably.
 
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1. What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object. It is a vector quantity that takes into account the mass, velocity, and distance from the axis of rotation.

2. Why is angular momentum important?

Angular momentum is important because it is conserved in a closed system, meaning it remains constant unless acted upon by an external force. This makes it a useful tool in understanding and predicting the behavior of rotating objects.

3. What does it mean for angular momentum to be conserved?

Conservation of angular momentum means that the total angular momentum of a system remains constant over time, even if individual components may change. This is due to the fact that the net torque acting on the system is equal to zero.

4. How is angular momentum conserved?

Angular momentum is conserved because of the law of conservation of angular momentum, which states that the total angular momentum of a closed system remains constant, as long as there is no external torque acting on the system.

5. What are some examples of conservation of angular momentum in everyday life?

Some examples of conservation of angular momentum in everyday life include the spinning of a top or a gyroscope, the motion of planets and satellites in orbit, and the movement of ice skaters or divers during a spin. In all of these cases, the angular momentum of the system remains constant, even as individual components may change.

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