An energetic golden hamster is running flat out at a constant speed on its frictionless exercise wheel. If the hamster is considered part of the exercise wheel system, how much work is being done on the hamster wheel system

The Hamster in a friction less exercise can move as fast as 10m/s at a constant speed  for wheel system

Explanation:

If the Energetic hamster keeps running faster, with less friction for a wheel system, there would be no limit for the hamster, until it starts approaching a light speed. A torque is not applied by The hamster to the wheel to move it, because the torque its self is a force, the torque is not a force that is stored up, it’s the angular velocity that is stored  

The relationship between a linear velocity and angular velocity is stated below

V= r w

If the hamster can move its leg in a fast way he can get to 10 m/s for a wheel system, finally, the hamster do nothing more than to so in the wheel at a speed that is constant.

Furthermore, the initial torque that is provided by the hamster deceases, then when the speed increases, the hamster will move faster as it can.