Rolling Mass on an Inclined Plane #2

[@akalsepaidal1591]

can u please make a video analyzing the motion of rolling objects up the incline plane?

[@harminderjitsinghtoor4579]

if fs is more than mg sin(theta) for smooth rolling, then body should be moving up the plane because net force is up the plane, isn't it?

[@TheScienceCube]

No but you must remember the fact that this is not linear motion only. The cylinder is rotating also and the friction force is actually providing the necessary torque. So you should not see the linear part in isolation

[@harminderjitsinghtoor4579]

@@TheScienceCube but newton’s law says that net acceleration of any body is in the direction of net external force. So I’m looking at net external force which is up the plane.

[@TheScienceCube]

@@harminderjitsinghtoor4579 The equation F = ma applies to rotating bodies as well. F gets substituted with torque and on the RHS we have angular acceleration and I. The force of friction will not pull the cylinder up the ramp. Instead, it will act to slow down the cylinder's descent. To understand why this is the case, it is important to remember that friction is a dissipative force. This means that it converts mechanical energy into thermal energy. As a result, the force of friction will always act to slow down the motion of an object. In the case of a cylinder rolling down an inclined plane, the force of friction will slow down the cylinder's rotation and translation. This will result in the cylinder losing energy and eventually coming to a stop. The force of friction can only slow down the cylinder, not reverse it.

[@TheScienceCube]

Understand what exactly is to roll smoothly and what is to roll with slippage. what is the mathematical condition for smooth roll?