A small ball rolls around a horizontal circle at height y inside a frictionless hemispherical bowl of

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A small ball rolls around a horizontal circle at height y inside a frictionless hemispherical bowl of radius R, as shown in Figure CP8.64.
a. Find an expression for the ball’s angular velocity in terms of R, y, and g.

b. What is the minimum value of ω for which the ball can move in a circle?

c. What is v in rpm if R = 20 cm and the ball is halfway up?

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