Is Mechanical Energy Conserved in Rolling Motion without Slipping?

[zorro]

Homework Statement

The Attempt at a Solution

In rolling without slipping, the friction does some work of torque about the axis of rotation. So mechanical energy is not conserved. A) - r),t)

B) and C) - r),t)

D) - One example I can think for the instant centre of rotation is the point of contact of a wheel rolling without slipping on a surface. No other force acts about the point of rotation.
So p),q),s) are the options here.

btw is there any difference between 'rolling' and 'rotating' about instantaneous axis of rotation?

answer for A) is incorrect.

 

[Doc Al]

In rolling without slipping, the friction does some work of torque about the axis of rotation. So mechanical energy is not conserved. A) - r),t)

Just because friction provides a torque about the center of mass does not mean it does work on the system. There is no displacement of the point of contact.

 

[zorro]

Thanks! I got it now.
But I still have a problem. Is my explanation for D) correct? Is it true that no external force does work about the instantaneous axis of rotation?