Angular Momentum Problem: Mouse walking on a rotating turntable

[thebeegchung721]

[Mentor’s note: moved from the technical forums so no template]

A turntable with a moment of inertia of 5.4x10-3 kg

m^2 rotates freely with an angular speed of 33 1/3 rpm. Riding on the rim of the turntable, 15cm from the center is a cute, 32g mouse. a) If the mouse walks to the center of the turntable, will the turntable rotate faster, slower, or at the same rate? Explain. b) Calculate the angular speed of the turntable when the mouse reaches the center. The axis of rotation is through the center of the turntable. What is the moment of inertia of the mouse? What is the total moment of inertia when the mouse is at the time of the turntable? What is the total moment of inertia when the mouse is at the center of the turntable?

If someone can help I'm stuck on part of this problem. It's assumed that angular momentum is conversed, so that means Li=Lf. In order to find Li, you find the angular momentum of both the turn table and mouse, and add them. Now since the mouse has no radius at the center, it has no momentum, so that part of the final momentum equation is zero. What confuses me however is finding the final angular speed of the turntable when the mouse reaches the center. The problem says no friction, so why isn't the angular momentum of the turntable the same initally and final? Is it because it essentially "loses" the weight of the mouse which causes it spin faster?

 

[A.T.]

Now since the mouse has no radius at the center, it has no momentum, so that part of the final momentum equation is zero.

1) Don't confuse momentum and angular momentum

2) If only mass is given for the mouse, then you are supposed to treat the mouse as a point mass. Look up the definition of angular momentum for a point mass around some reference point, and calculate the angular momentum of the mouse around the turntable center based on that.

The problem says no friction...

It doesn't mention bearing friction at the turntable axle, so that can be assumed to be zero. It says the mouse walks to center, so there must be static friction at the mouse feet.

so why isn't the angular momentum of the turntable the same initally and final?

The total angular momentum of mouse and turntable stays the same, but since the total moment of inertia changes, the angular velocity must also change.

 

[Chestermiller]

A turntable with a moment of inertia of 5.4x10-3 kg

m^2 rotates freely with an angular speed of 33 1/3 rpm. Riding on the rim of the turntable, 15cm from the center is a cute, 32g mouse. a) If the mouse walks to the center of the turntable, will the turntable rotate faster, slower, or at the same rate? Explain. b) Calculate the angular speed of the turntable when the mouse reaches the center. The axis of rotation is through the center of the turntable. What is the moment of inertia of the mouse? What is the total moment of inertia when the mouse is at the time of the turntable? What is the total moment of inertia when the mouse is at the center of the turntable?

If someone can help I'm stuck on part of this problem. It's assumed that angular momentum is conversed, so that means Li=Lf. In order to find Li, you find the angular momentum of both the turn table and mouse, and add them. Now since the mouse has no radius at the center, it has no momentum, so that part of the final momentum equation is zero. What confuses me however is finding the final angular speed of the turntable when the mouse reaches the center. The problem says no friction, so why isn't the angular momentum of the turntable the same initally and final? Is it because it essentially "loses" the weight of the mouse which causes it spin faster?

Let's see your equations.

 

[kuruman]

In order to find Li, you find the angular momentum of both the turn table and mouse, and add them. Now since the mouse has no radius at the center,

But the mouse is initially

Riding on the rim of the turntable, 15cm from the center

Doesn't that count as the radius for the initial angular momentum of the mouse?

 

[haruspex]

But the mouse is initially

Doesn't that count as the radius for the initial angular momentum of the mouse?

If you read on in post #1:

so that part of the final momentum equation is zero

so @thebeegchung721 is not referring to finding Li.

The problem says no friction

No friction where? Please quote the exact wording.

 

[kuruman]

so @thebeegchung721 is not referring to finding Li.

Yes, I see now. It didn't occur to me that the OP has difficulty writing an expression for the final angular momentum when all the angular momentum is in the turntable.