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A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a hole in the table, where I'm holding it. Initially, the particle is moving in a circle of radius r0 with angular velocity w0, but I now pull the string down through the whole until at length r remains between the hole in the particle.

(a) What is angular velocity of the particle now?

(b) Assuming that I pull the string so slowly that we can approximate the particles that my circle of slowly shrinking the radius, calculate the work I did pulling the string.

(c) Compare your answer with part (b) with the particles gain in kinetic energy.

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