When a man is doing ice skating and rotating on his toe, with his arms widespread, his angular velocity is less, in comparison to the angular velocity when he is rotating with his arms closed inside. Now suppose man is turning his hands slowly inwards, so his angular velocity will start to increase, now there is no external torque on the man but his angular velocity is increasing and increasing angular velocity will have an associated angular acceleration, so we can conclude that the man has angular acceleration without any external torque, which is an apparent contradiction of the terms, so how do we reconcile the case with the concept?
Can we explain this case without using the concept of "Angular Momentum Conservation"? because that encapsulates a lot of details, without giving the complete clarity.
Best Answer
The definition of torque is not $\tau=Id\omega/dt$. We can't even define things like $I$ and $\omega$ for rotation that isn't rigid.
The definition of torque is $\tau=dL/dt$. So yes, it is possible to have an angular acceleration without an external torque. Your example shows correctly that this can happen.