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A small car of mass m travels on the inside of a frictionless vertical circular track...

A small car of mass m travels on the inside of a frictionless vertical circular track of radius R. The speed of the car v is big enough to keep it on the track all the time. (a) What is the magnitude of the normal force N on the car at a position that makes an angle θ with the vertical? (b) What is the magnitude of the angular acceleration α of the car at the same position? (c) Assume that the speed of the car at the top point is just enough to keep it on the track (Hint: Then N=0). How much is that speed? (d) What is then the speed at the bottom point of the track? (Hint: Use conservation of energy.) (e) What is the magnitude of the normal force at the bottom point?

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