Suppose you swing a ball of mass m in a vertical circle on a string of length L

Question

Suppose you swing a ball of mass m in a vertical circle on a string of length L. As you probably know from experience, there is a minimum angular velocity ?min you must maintain if you want the ball to complete the full circle without the string going slack at the top.

Show steps please if possible.

Find an expression for omega min in terms of g and L Express your answer in terms of the variables L and appropriate constants. Evaluate omega min in rpm for a 65 g ball tied to a 1.4-m-long string. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

using given formula wmin= sqrt(g/l)= sqrt(10/1.4)=2.67 rad/ sec

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