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Why is the direction of friction on an inclined plane always "up the incline" when a body goes up or down the plane with pure rolling motion?enter image description here

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  • $\begingroup$ In both the cases when there is no external force other than gravity, the friction will always work against the only external force gravity. $\endgroup$
    – Alapan Das
    May 10, 2020 at 12:33

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Case 1: Ball rolls up the plane. Gravity retards the ball, so its linear velocity will decrease. In order to prevent slipping, angular velocity should also decrease. So friction should provide a torque opposite to the rotation of the ball. This direction turns out to be up the plane at the lower most point of the ball. The diagram should make it understandable. enter image description here

Case 2 : Ball rolls down the plane. In this case gravity accelerates the particle. So its linear velocity increases. In order to keep up, its angular velocity must also increase. Friction provides torque to increase angular velocity, which turns out to be up the plane as well.

enter image description here

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