# Work done by static friction in Rolling

In rolling without slipping, I understand that the velocity of the point where static friction with the ground is 0, and therefore static friction cannot do work. However, from newtons laws, an object rolling without slipping on a level surface is experiencing static friction - and thus an acceleration. This means the object will come to a stop over time. As a result, delta K is not 0, so how does this not contradict work energy theorem?

Suppose, some external force is accelerating a body and the body is still rolling without slipping. Now, if the velocity increases without increase in angular velocity, the body will slip. Then, friction acts in such a way that it opposes the transnational motion of the body and increases angular speed, effectively transferring some of the work done by the external force to the energy of rotation.

Suppose there is no external for (other than friction) and the body is rolling without slipping. Then the velocity at point of contact is zero, and therefore the friction is zero. So no work is done by friction and the net force on the body is zero. Then the body will not lose energy.

However, in a real scenario, a body rolling without slipping without any external force eventually slows down due to friction. This is due to the fact that the body is deformed at the point of contact due to the normal force and this requires some energy. Later, this energy is dissipated in the form of heat.

• Nonetheless, if the friction force exists (which it does), and thus accelerates (whether it slows to a stop or not is irrelevant) there is a change in kinetic energy. This requires some work.
– user225234
Commented Jul 4, 2019 at 13:29
• Additionally, there is still friction on the bottom point with 0 velocity. Think of pushing on a heavy block that is not moving, it is not moving because static friction is preventing its motion.
– user225234
Commented Jul 4, 2019 at 13:34
• I’m this instance, rotational kinetic energy and translational kinetic energy change together (was given by $v=r\omega$ Thus energy can not be transferred between the two quantities.
– user225234
Commented Jul 4, 2019 at 18:38
• I have edited my answer. Commented Jul 5, 2019 at 4:34
• How can you say friction is zero - friction is what provides the torque for rotation. Without it the object would simply slide.
– user225234
Commented Jul 6, 2019 at 5:42