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Assume a ball to be kept on a rough surface with intial translational velocity V and no rotation. After some time it aquires pure rolling. It is acted upon by an external torque due to friction still the angular momentum of the ball does not change from that of the initial one. Why is this?

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  • $\begingroup$ Why do you say the angular momentum is conserved? $\endgroup$ – Manish S Dec 20 '20 at 14:02
  • $\begingroup$ Angular momentum of an isolated system is always conserved. $\endgroup$ – my2cts Apr 5 at 12:57
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Angular momentum depends on the axis chosen. If the axis is chosen at the point where the friction force acts on the rolling body, then the perpendicular distance of the friction force from the chosen axis will be zero at all times and hence the torque due to the friction force shall be zero. As no other external force is mentioned in the question, the net torque about the chosen axis shall be zero and hence angular momentum about the chosen axis will remain constant throughout.

However if some other axis is chosen, then the torque due to the friction force about the axis shall be non-zero and then the angular momentum about the axis shall change. It will not be constant.

Hope this answers your question.

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  • $\begingroup$ Good answer. Actually for a simple calculation any point on the horizontal surface in line with the direction of motion can be taken as the reference point. Then: L = mvR + Iω. $\endgroup$ – R.W. Bird Apr 5 at 15:00

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