Constant rotational kinetic energy

[fib1123]

A mass m is attached at the end of the string. The mass moves on a frictionless table, and the string passes through a hole in the table, under which someone is pulling on the string to make it taut at all times. Initially , the mass moves in a circle, with kinetic energy [E][/0] . The string is slowly pulled, until the radius of the circle is halved. How much work is done?

I calculated the work and the result is

but my question is: Why is the rotational kinetic energy constant during the motion?

 

[A.T.]

A mass m is attached at the end of the spring.

String?

Why is the rotational kinetic energy constant during the motion?

Work is done, so kinetic energy must change. The angular momentum is constant, because there is not torque.