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When a ball rolls down without slipping on a ramp, the static friction is pointing upwards along the ramp, providing the torque for rolling. No problem with that.

However, if a ball has initial velocity and rolls down with slipping, the kinetic friction will come into play. My question is, is the friction pointing upwards or downwards, and why?

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If the ball is slipping when starting from rest it means that the ball is rotating too slowly relative to the linear speed of its centre of mass.
The friction force will be in such a direction as to try to reduce the relative speed between the point of contact of the ball and the slope.
The frictional force does this by reducing the linear acceleration of the centre of mass of the ball whilst increasing the angular speed of the ball (about its centre of mass.
Thus the frictional force acts upwards along the slope in the opposite direction to the component of the weight of the ball down the slope and provides a torque to increase the angular speed of the ball.

So the condition the ball is trying to reach is no relative movement at the point of contact between the ball and the slope - no slipping.

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