A particle of mass m is moving on a frictionless horizontal table and is attache

Question

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 am holding it. Initially the particle is moving in a circle of radius r0 with angular velocity ?0, but I now pull the string down through the hole until a length r remains between the hole and the particle. (a) What is the particle's angular velocity now? (b) Assuming that I pull the string so slowly that we can approximate the particle's path by a circle of slowly shrinking radius, calculate the work I did pulling the string. (c) Compare your answer to part (b) with the particle's gain in kinetic energy

Explanation / Answer

Angular momentum conservation m*(r0)^2*(w0)=m*(r)^2*(w) a>>so, w=(w0*r0^2)/r^2 b>>work done = Force*displacement= m*w^2*r*r - mw0^2*r0*r0 c>> same as b>>

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