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

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Discussion Overview

The discussion revolves around the forces experienced by point B of a rotating rod when a force is applied at point A. Participants explore the mechanics of rotation, the effects of applied forces, and the interactions with a mass placed near point B. The scope includes theoretical reasoning, mathematical modeling, and conceptual clarifications related to rotational dynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant queries the force felt by point B when a momentary force is applied at point A, suggesting that B must experience some force due to its movement.
  • Another participant questions whether point B is treated as a point mass or a finite piece of the rod with mass, indicating the need for clarity on the system's configuration.
  • A suggestion is made to analyze the force experienced by a ball placed next to B, emphasizing that the system is frictionless.
  • Participants discuss the application of Newton's second law and the computation of motion for point B.
  • Torque and angular momentum equations are introduced, with a focus on the moment of inertia of the rod and its implications for angular acceleration.
  • Concerns are raised about the omission of the torque exerted by the contact force of the ball on the rod, questioning its inclusion in the angular momentum equation.
  • Two perspectives are offered regarding the ball's role: as a test object or as an anchor point, each leading to different interpretations of the forces involved.
  • Clarifications are made regarding whether the ball is physically attached to the rod or simply in contact, with implications for the analysis of forces and accelerations.
  • One participant expresses a desire to avoid overly complex interpretations of the interaction between the rod and the ball, suggesting a simpler model where the ball is just pushed by the rod.
  • Concerns are raised about the implications of the ball's mass relative to the rod and the necessity of accounting for the contact force in the analysis.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact nature of the forces involved, with multiple competing views on the role of the ball and the necessary considerations for the analysis. The discussion remains unresolved regarding the specific forces acting on point B and the implications of the ball's interaction with the rod.

Contextual Notes

Limitations include assumptions about the configuration of the rod and ball, the nature of the applied forces, and the treatment of the ball as either a point mass or a more complex object. The discussion also highlights unresolved mathematical steps in the analysis of torque and angular momentum.

  • #31
Adesh said:
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?"
 
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  • #32
jbriggs444 said:
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.
 
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  • #33
jbriggs444 said:
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?
 

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