What force will be felt by ##B## when a rod is rotated?

[jbriggs444]

Thank

Thank you so much sir, thank you so much. You have helped me very nicely.

Getting back to your original question about force. Perhaps we can rephrase it.

"What force applied at the near end of the rod would be required to produce the same near-end acceleration as force F applied at the far end of the rod?"

 

[Adesh]

Getting back to your original question about force. Perhaps we can rephrase it.

"What force applied at the near end of the rod would be required to produce the same near-end acceleration as force F applied at the far end of the rod?"

Yes, that what I meant.

I learned these things from this thread:

1. Angular acceleration of all points on a rotating body is same.

2. Acceleration of all points on a rotating body is not same.

3. It’s important to know where the force is applied, we do care about the moment (torque) it produces.

4. The most important thing: when we get some doubt we begin to suspect every clause of our writing, we fear if we are wrong.

 

[etotheipi]

For a small test ball being pushed continuously by the tip of the rod, Newton's second law applies.
If the ball is big enough to affect the motion of the rod, you have a different problem to solve. You should start by computing the position of the center of mass of the ball+rod.

This is the part that I wasn't following, you were computing the equations of motion for the rod under the approximation that the force of contact between the ball and rod is small enough to be ignored for the dynamics of the rod (reasonable if $m$ of the ball is small), but considered for the ball for which that is the only force acting on it.

I must say even considering the problem without this approximation (i.e. we now compute the motion of the rod accounting for the contact force), the problem isn't exactly intuitive to me. Without any friction, can you push the ball by rotating the other end of the rod without the ball just accelerating and then losing contact? Or are we only considering a small period of time during which the configuration is approximately fixed?