Problem 5.

A small body of mass is attached to a light thread which passes through a hole at the centre of a smooth table. The body is set into rotation in a circle of radius , with a speed of . The thread is then pulled down shortening the radius of the path to . What will the new linear speed and the new angular speed be?

Solution:

In the present problem we have conservation of the angular momentum. The initial angular momentum is

The final angular momentum is

Since then

From this equation we can find the final speed of the body

The angular speed can be expressed through the linear speed and the radius of circle:

Then