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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.

Floris
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Anonymous
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1 Answers1

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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.

user141412
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    Will a body roll in smooth inclined plane – Anonymous Jan 10 '17 at 07:10
  • You mean a frictionless inclined plane like Teflon? No, indeed not, it would just slide and accelerate, but not pick up rotation. Indeed the angle of the force acting through the point where roll and plane would touch would be different. So, indeed concerning your original wording, if the plane is not frictionless, the force acting in this point is not normal, i.e. not going through the center of the roll. If the plane is Teflon, then the force is normal. The difference between those two forces is indeed the friction. – user141412 Jan 10 '17 at 07:18
  • In problems involving smooth parabolic or curved paths rotation is taken under consideration . Why? – Anonymous Jan 10 '17 at 10:51
  • We are still talking about an inclined ramp? If "smooth" is describing just the shape of the curve of the ramp and notsaying that it's frictionless, i.e. we assume no slip, then the rotation just depends on the final speed, and the final speed just depends on the initial height from which you start. (i.e. the potential energy). The exact shape of the inclined path is not important. – user141412 Jan 10 '17 at 12:38
  • But provides the torque to maintain the relation between angular acceleration and acceleration of centre of mass – Anonymous Jan 11 '17 at 04:35