I ran across a conceptual problem while solving this situation:
A marble is sliding down from the top of a larger sphere, at what angle from the vertical will it leave the sphere?
I solved the problem by using the fact that the marble will leave the sphere when the radial component of the gravitational force is equal to the centripetal force the marble is experiencing. My problem is this: why is there centripetal acceleration at all?
I understand that the marble is moving in a circular path while on the sphere, but why doesn't all of the gravitational force in the radial direction go into the normal force? I know this would mean that the only force acting on the marble would be a tangential force so it's not correct, but why?
I guess my problem with it is that if we were to pick up the marble and place it an inch further on the sphere, there wouldn't be a centripetal force, all of the radial force would be normal; so when does it become centripetal and why? Also, isn't circular velocity increasing as the ball falls, so wouldn't that change the centripetal acceleration?
Sorry if this question is a bit trivial, but I'm just confused. Thank you in advance for your help.