# Energy conservation in rotational motion

When a disk is in pure rolling, can the energy be conserved? And if the disk is in pure rolling on the inclined plane, there is static friction acting on the disk then how can the energy be conserved there?

The velocity of point of contact of disc and surface is zero which means that the point of contact doesn't get displaced in rolling motion.

The point of application of friction is the point of contact of disc and surface.As this point doesn't get displaced which means that static friction does no work which ensures law of conservation of mechanical energy.

Static friction is by its very nature unable to move anything anywhere. It is keeping the contact point stationary - nothing moves where the force acts. The rest of the ball moves, yes, but not the contact point.

So static friction does no work (hence neither increases nor decreases the energy of system). A ball rolling is influenced by static friction as the force that start rotation, but only other forces such as the weight (which is conservative) can do work.

• So when a disk has only linear velocity and kept on the floor the static friction act on it then can the energy be conserved. May 13, 2020 at 8:57
• Yes, as long as there are no other dissipative forces. May 13, 2020 at 9:01
• Is the rolling is accelerated can the energy be conserved. (disk in SHM with a spring attached to iton COM) May 13, 2020 at 9:01
• In SHM, energy always remains conserved. May 13, 2020 at 9:04
• How can i attach photo of a question May 13, 2020 at 9:06