What is the direction of Friction when a sphere rolls up or down an inclined plane?

Dear ashutosh

no friction is involved in uniform rolling.  friction is actually the agent, which enforces the condition for accelerated rolling. In doing so, friction causes linear and angular accelerations or decelerations, depending on the requirement of rolling motion.

When the external force is passing through center of mass, it only produces linear acceleration as there is no moment arm and, thus, there is no torque on the body. Linear acceleration means linear velocity tends to increase. This, in turn, induces tendency of the rolling body to slide in the forward direction (i.e. in the direction of force/acceleration). Force of friction, therefore, appears in the backward direction of external force to check the sliding tendency

 

Now, we consider the second case.  The external force that does not pass through center of mass causes angular acceleration apart from causing linear acceleration. The force has dual role to play in this case. As far as its rotational form (torque) is concerned, resulting angular acceleration means that angular velocity tends to increase. This, in turn, induces tendency of the rolling body to slide in the backward direction (i.e. in the opposite direction of force). Force of friction, therefore, appears in the direction of external force to check the sliding tendency

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Badiuddin

direction of frictional force is alwayas opposite to rotation