Rotation from Oscillating Axis Of Rotation

AI Thread Summary
A rod rotating about its end on a moving axle experiences spinning due to the periodic linear motion of the axle. This motion imparts tangential velocity to the rod when the axle changes direction, resulting in torque applied relative to the rod's center of mass. The rod oscillates and rotates simultaneously, except at two positions where the axle's direction aligns with the rod, minimizing torque. The discussion highlights the interplay between linear motion and rotational dynamics in this scenario. Understanding these mechanics is crucial for analyzing similar systems.
Omikhiro
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Hello. I was considering a case where a rod could rotate about its end freely on an axle. The axle is moved back and forth linearly and periodically, causing the rod to spin.

Why is the rod spinning? Is it because after the axle has moved its distance in one direction and has stopped to move in the other direction, it is adding tangential velocity to the rod?
 
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I sketch showing the motion would equal many words.
 
It is applying torque with respect to the COM of the rod except two positions where the direction of oscillations align with the rod, thus the rod rotates and oscillates at the same time.
 

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