# Angular Momentum of a turntable with frictionless bearings

• chara76
In summary: This means that the total angular momentum before the catch equals the total angular momentum after the catch. In summary, during the catch on a turntable with frictionless bearings, the angular speed of the turntable increases, the magnitude of the person's angular momentum increases, the ball's angular momentum decreases, and the total angular momentum of the system remains the same.
chara76

## Homework Statement

You are standing on the edge of a turntable with frictionless bearings. It is initially rotating when you catch a ball, which is moving in the same direction but faster than you are moving and on a line tangent to the edge of the turntable. Assume you do not move relative to the turntable.

(a) Does the angular speed of the turntable increase, decrease or remain the same during the catch?
I know this increases

(b) Does the magnitude of your angular momentum (about the rotation axis of the turntable) increase, decrease, or remain the same during the catch?
I know this increases as well

(c) How does the ball's angular momentum (about the rotation axis of the table) change after the catch? Increase, decrease, or remain the same?
This decreases (ball comes to a stop)

(d) How does the total angular momentum of the system, you-table-ball (above the rotation axis of the turntable), change after the catch? Increase, decrease, or remain the same?
Without actual numbers, I am having trouble trying to figure this one out in my head. Any ideas?

## The Attempt at a Solution

(c) You are right that it decreases, but the ball didn't come to a full stop. It is now traveling with you around in a circle.

(d) Don't forget that the total angular momentum is conserved.

## 1. What is Angular Momentum?

Angular momentum is a property of a rotating object that describes the amount of rotational motion it possesses. It is a vector quantity that takes into account the mass, speed, and distance from the axis of rotation.

## 2. How is Angular Momentum calculated?

Angular momentum is calculated by multiplying the moment of inertia (a measure of an object's resistance to rotational motion) with the angular velocity (the rate of change of the angle of rotation). The formula for angular momentum is L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.

## 3. What is the significance of frictionless bearings in relation to the Angular Momentum of a turntable?

The presence of frictionless bearings in a turntable allows for the conservation of angular momentum. This means that once the turntable is set in motion, it will continue to rotate at a constant speed without any external force or torque acting on it. This is due to the absence of friction, which would otherwise slow down or stop the rotation of the turntable.

## 4. How does the Angular Momentum of a turntable change when a force is applied?

If a force is applied to the turntable, the angular momentum will change. This is because the force will cause a torque (a twisting force) on the turntable, which will result in a change in the angular velocity. The new angular momentum can be calculated by using the formula L = Iω, where I is the new moment of inertia and ω is the new angular velocity.

## 5. How does friction affect the Angular Momentum of a turntable?

If there is friction present in the bearings of a turntable, it will cause a decrease in the angular momentum over time. This is because friction will generate a torque that acts in the opposite direction to the rotation, resulting in a decrease in angular velocity. As a result, the turntable will eventually come to a stop unless a force is applied to counteract the frictional torque.

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