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A block of mass m is moving in a circular path on a tabletop. The radius...

A block of mass m is moving in a circular path on a tabletop. The radius of the circle is r and the object's speed is v. What is the initial angular momentum of the system? What is the initial kinetic energy of the system?

Suppose the mass was being pulled in circular motion by a string. The string is threaded through a small hole on the top of the table, and a person pulls on the string until it has a length of r/3.

What is the new angular momentum of the system? What is the new speed of the mass? What is the new kinetic energy of the system? Comparing kinetic energies, how much work was done?


Find the change in kinetic energy a second way, by integrating the work done as the mass is pulled inwards. To do this you will need to integrate a force over a displacement. The force in question will be the tension in the string, which is equal to the centripetal force as a function of string length. This can be calculated by observing that angular momentum is conserved, so velocity is a function of string length.

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