Question

Are translational and rotational kinetic energy same if a rigid body is rolling without slipping on inclined plane?

Answer 1

there is no frictional energy dissipation as the cylinder moves over the surface. This is only possible if there is zero net motion between the surface and the bottom of the cylinder, which implies , or 

It follows that when a cylinder, or any other round object, rolls across a rough surface without slipping--i.e., without dissipating energy--then the cylinder's translational and rotational velocities are not independent, but satisfy a particular relationship (see the above equation). Of course, if the cylinder slips as it rolls across the surface then this relationship no longer holds.