A marble on the end of a massless string is rotating about a hole at O on a flat

Question

A marble on the end of a massless string is rotating about a hole at O on a flat(horizontal) frictionless table. The mass originally rotates with an angular velocity theta'=w0 and r is constant at r1. At some time t0 the string begins to be pulled into the hole(at O) until the length of the string reaches its new (shorter) length of r2, where it remains constant(while the marble continues to rotate about O). What is theta' when the string reaches the length r2? A marble on the end of a massless string is rotating about a hole at O on a flat(horizontal) frictionless table. The mass originally rotates with an angular velocity theta'=w0 and r is constant at r1. At some time t0 the string begins to be pulled into the hole(at O) until the length of the string reaches its new (shorter) length of r2, where it remains constant(while the marble continues to rotate about O). What is theta' when the string reaches the length r2?

Explanation / Answer

initial angular momentum = mr1^2*w0 final angular momentum = mr2^2*w angular momentum conservation, so w = w0*(r1/r2)^2

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