Question

We assumed the pulley is massless. In reality, it has some mass, which means it has some kinetic energy (and, presumably, this kinetic energy increases as you go faster).1 Since the pulley does in fact have some mass, what impact would this have on the slope of our energy vs. time plot?

Answer 1

For the development of a problem with pulleys, it is based on the fact that this is a conservative force, which is ultimately neglected for its insignificance. The mass of a pulley plays an insignificant role, which is summed up to several decimal digits, if compared to the mass that is being lifted.

The only case in which this mass affects an E vs. t graph will only be when the mass of the raised object approaches that of the pulley mass and whose force is close to that necessary to break the pulley inertia and begin its movement.

In the event that the pulley moves with constant angular velocity, the pulley mass will lose effect as the pulley will not have any type of acceleration. In Newton's second law this would cause the force to simply become 0 when there is no force of inertia.

But if the pulley moves at a constant angular speed, the mass of the pulley will have no effect, since there will be no angular acceleration and, therefore, there will be no inertia and, therefore, there will be no force of inertia.