Posted by Andrew on Sunday, September 5, 2010 at 2:37am.
If there were no friction, the marble would slide, not roll. It is not clear which way they want this problem to be done.
In either case, a formula for the velocity of the marble vs. angle from the top can be derived. The rolling and sliding (no friction) cases will be different.
The marble will remain in contact with the bowling ball until
M g cos theta = M V^2/R
cos theta = V^2/(g R)
Knowing V(theta), you can solve for theta.
Although friction is needed to make the ball roll, it does not remove kinetic energy, because there is no "slipping" motion at the point of contact.
crap
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