A student spins a bicycle wheel that is mounted on a frictionless horizontal axle. After a few seconds the wheel is observed to rotate at constant angular speed even though the student continues to press her finger lightly against the tire’s sidewall.
The contact between the finger and the rubber surface provides a torque about the axle that is opposite the direction of rotation, yet the wheel’s kinetic energy does not change once constant speed is reached.
(a) Describe, in words, the mechanical conditions under which a non-zero torque acting on a rigid body does no net work on that body over a finite time interval.
(b) Explain why the finger’s torque does no net work on the wheel once the wheel has reached constant angular speed, even though the torque is not zero.
(c) Would the answer to part (b) change if the student’s finger were instead slipping against the tire so that the rubber surface slides under the finger? Justify your reasoning without using equations.