How Does Catching a Ball Affect Angular Momentum and Speed on a Turntable?

[sonutulsiani]

Homework Statement

You are standing on the edge of a turntable with frictionless bearings that is initially rotating when you catch a ball that 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 on the turntable.


1. What happens to the angular speed of the turntable during the catch?

A. It increases.
B. It decreases.
C. It remains the same.


2. What happens to your angular momentum during the catch?

A. It increases.
B. It decreases.
C. It remains the same.


3. What happens to the angular momentum of the ball during the catch?

A. It increases.
B. It decreases.
C. It remains the same.


4. What happens to the total angular momentum of the entire system (turntableyou- ball) during the catch?

A. It increases.
B. It decreases.
C. It remains the same.

Homework Equations

The Attempt at a Solution

Please help me with this. Can't figure it out.

 

[Andrew Mason]

Start with the definition of angular momentum:

(1) $$\vec L = m \vec v \times \vec r$$

If v is purely tangential as it is here then $\vec L = = m|v|r \hat{n}$

and this definition of angular velocity:

(2) $$\vec \omega r^2 = \vec v \times \vec r$$

You can also use:

(3) $\omega = v_T/r$ where $v_T$ is the tangential speed.

1. is pretty easy. Ask yourself: when I catch the ball, do I speed up, slow down or is there no change? What does that do the angular speed? (Hint: use the above equations. Since r does not change, if tangential speed increases, what happens to $\omega$?)).

2. What happens to the mass on the turntable when I catch the ball? What happens to $\vec L$ in equation (1) if angular speed changes as you have found in 1. and the mass changes?

3. Is somewhat tricky because the ball has angular momentum before it is caught. Use (1) to determine what that is. What happens to the ball's speed? How does that affect L in equation (1)?

4. This is the most important question. Can you show that angular momentum is conserved?

AM

 

[sonutulsiani]

1. It's increasing

2. Since angular speed increases, angular momentum also increases?

3. I didn't get it. If the ball has momentum before, so it should increase?

4. It's same

 

[Andrew Mason]

1. It's increasing

2. Since angular speed increases, angular momentum also increases?

Why the question? Since L = mvr, what happens to L if v increases?

3. I didn't get it. If the ball has momentum before, so it should increase?

Does the ball speed up or slow down when it is caught? So what happens to its angular momentum: L = mvr ?

AM

 

[sonutulsiani]

2 is increasing.

And 3 will be decreasing