Homework Help: A rolling ball

1. Jan 10, 2013

sapz

1. The problem statement, all variables and given/known data
Hi

Im trying to solve this question, and I have the solution of it in front of me, but I really cant understand why its true.

The question is this: A bowl with radius R is given, it cant move. In it there's a ball with radius r << R, and a mass m.
Find... (lots of subclauses for the question)
A picture is attached.

My question is this:
Am I mixing the directions of the forces/torques?

F is the friction force. I think the torque equation should be I*w_dot=F*r.
and the equation for the tangential direction should be ma=F-mgs*sin(theta).

However, in the solution I see here the torque equation appears with a minus sign: I*w_dot=-F*r, which obviously changes the answers of the things I need to find.

Should it be with a minus? Or without? Thank you.

2. Relevant equations

3. The attempt at a solution

Attached Files:

• rolling.png
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2. Jan 10, 2013

haruspex

This doesn't look right to me at all. If we take moments about the centre of the ball, there is indeed a torque Fr anticlockwise, and it does tend to reduce theta. But $\ddot{\theta}$ is not the angular acceleration of the ball.
There should be another angle in the picture - the angle through which the ball has rotated. It is related to theta by a simple formula.