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*without slipping.*The bowl has radius L and the ball has radius R. I need to write down the constraint relating the angular velocity of the ball, call it omega , to the angular velocity the center of the ball is sweeping out in the bowl. Theta is the angle between the line from the center of the bowl to the center of the ball and the vertical. So I need the relationship between omega and the time derivative of theta.

My professor is being extremely stubborn and claiming that the constraint equation is:

[tex] \omega = L\theta/R [/tex]

But it actually should be this:

[tex] \omega = (L-R)\theta/R [/tex]

Is there anything short and to the point I can say for him to listen to me? I've sent a long explanation to him but he simply dismisses me and tells me to keep thinking about the problem.