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When the axis of rotation is fixed, the angular momentum is given by:

${\vec{L}=\vec{L}_z+\vec{L}_\bot}$
Where: ${\vec{L}_z}$ is the component parallel to the axis of rotation. ${\vec{L}_\bot}$ is the component perpendicular to the axis of rotation.

When we differentiate this expression, we get the torque experienced by the rotating body.
So ${\frac{d \vec{L}}{dt}=\vec{\tau}}$
The text book says: ${\frac{d \vec{L}_\bot}{dt}=0}$
That is., differentiating the last term in ${\vec{L}=\vec{L}_z+\vec{L}_\bot}$ will give zero.
I am unable to understand why it becomes zero.
Please help me. Thanks.

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  • $\begingroup$ In this situation is the object constrained to a circular path? $\endgroup$ – electronpusher Aug 25 at 14:59
  • $\begingroup$ Yes. The object moves in a circular path. Also, the axis of rotation is fixed. $\endgroup$ – Nikhil Kumar Aug 25 at 15:48

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