Rolling in smooth inclined plane

Question

Can a body posses pure rolling in smooth inclined plane.In smooth inclined plane the centre of mass of body is accelerating.So to maintain the pure rolling there should be angular acceleration.But no one provides the torque because the only forces Gravity and Normal reaction passes through centre.

Answer 1

Whenever a simple roll starts rolling on earth, it is the earth itself that provides the angular momentum. In your case, the roll on the say, for example, 30 degrees inclined plane always exerts its force perpendicular to the plane, i.e.pointing at (90-30)= 60 degrees into the earth. That means your roll kicks the earth a little sideways. So if your roll rolls to the east, it pushes the earth a bit to the west. If you would install your inclined plane say on a large cartwheel at rest, then indeed the cartwheel would behave like the earth and to rotate in the opposite direction as your roll.

You asked also how does the angular momentum get into the roll: The fact is that the different parts of the roll feel different resulting forces. The part closer to the plane experiences gravity, but also the restoring force from the resting point on the plane, while the part further away from the plane just experiences gravity and "drops" therefore. so you have a similar distribution of force as with a crank, which acts only on one side of a roll.