Work of friction on rolling objects

Question

In many cases when there is friction acting on a body which is rolling without slipping ( for eg : a body rolling down a inclined plane ),

We say, that the work done by the friction is zero as the velocity of point in contact is zero adn it works out.

But the question,I am having is how does friction still comes into play while the relative velocity of the point is zero ? , because as we know when relative velocity is zero , friction shouldn't act. But if the later is only true after friction comes into play then why does it still keep acting after the relative velocity is zero?

Answer 1

because as we know when relative velocity is zero , friction shouldn't act.

This is false. Static friction acts when the relative velocity between surfaces is $0$. For a simple example, take a heavy object and start pushing on it without it moving. Static friction is the force that opposes your applied force before the object starts moving.

Because of this, it is in fact true that static friction does not do work on a rolling object in the rest frame of the surface the object is rolling across.

Answer 2

If you are accelerating in your car, then the friction force from the road acting in the forward direction on the bottom of the wheels is moving forward with your car. As the only net external force, it is doing the work to accelerate the car. If you apply the breaks, the friction force acts backwards, moves with the car, and does negative work to remove the cars kinetic energy. If a wheel is rolling down an incline, friction provides the torque to increase the rotational energy.
In each of these cases, the object is gaining or losing energy in the rest frame. Clearly, there is something wrong with the logic that says that static friction cannot do work.