Dumb question about inertia and rotational inertia

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Discussion Overview

The discussion revolves around the effects of a repulsive force on two bodies, one spinning and one at rest, particularly focusing on their linear and rotational motions. Participants explore concepts of inertia, angular momentum, and the implications of applying forces at different points on the bodies.

Discussion Character

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

Main Points Raised

  • Some participants propose that both bodies will be displaced at the same speed due to the nature of linear and angular momentum being different quantities.
  • Others argue that the spinning body offers resistance to changes in its axis of rotation, which could affect the outcome.
  • There is a suggestion that if the repulsive force is applied at one extremity of the spinning body, it could lead to a change in its rotational state.
  • Some participants discuss the implications of applying force at different points, noting that off-center forces can lead to different rotational effects.
  • One participant questions whether the spinning body would move away at a different speed than the non-spinning body, suggesting that the spin might affect the resistance to movement.
  • There are discussions about the stability of orientation due to angular momentum and how that interacts with linear motion when forces are applied.
  • Participants consider scenarios involving parallel pipes and bicycle wheels to illustrate the effects of force application on linear and rotational motion.
  • Some participants express uncertainty about the outcomes, indicating that the question may not have a straightforward answer.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as multiple competing views remain regarding the effects of the repulsive force on the spinning and non-spinning bodies. The discussion reflects uncertainty and varying interpretations of the physical principles involved.

Contextual Notes

Limitations include unresolved mathematical steps regarding energy distribution between linear and rotational motion, as well as dependence on the definitions of stability and resistance in the context of rotational dynamics.

Who May Find This Useful

This discussion may be of interest to those studying physics, particularly in the areas of mechanics, rotational dynamics, and the effects of forces on motion.

  • #31
I think that the premise of the OP was an equal force, not equal energy. If you apply the same force over the same time on the end as you would at the center of mass, the end will accelerate more and move farther. That means more work is done, so more kinetic energy is put into the motion.

You can calculate the kinetic energy. In all cases, the center of mass reacts according to ##F = mA##. Depending on how long the force is applied, that gives you the amount of linear kinetic energy. The rotational kinetic energy can be calculated using the duration of the force, the torque and the inertial moments.
 
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  • #32
FactChecker said:
I think that the premise of the OP was an equal force, not equal energy.
That's why I was thinking of starting a new thread.
FactChecker said:
In all cases, the center of mass reacts according to ##F = mA##.
Intuitively, it seems wrong to me that applying a (force x distance) to the edge of the pipe would result in the same linear kinetic energy as applying the same (force x distance) to the center of mass, although I don't know how to prove it one way or the other.

Edit: Actually now that I think about it, I'll try approaching it in a collision/conservation of momentum framework instead, perhaps that'll make things clear to me.
 
  • #33
snoopies622 said:
Intuitively, it seems wrong to me that applying a (force x distance) to the edge of the pipe would result in the same linear kinetic energy as applying the same (force x distance) to the center of mass
Intuitively, if you push on one end, that end will move more than if you were pushing at the center. But the other end will move less than if you were pushing at the center. The motion at the center will be the average of the motions at the two ends, which is exactly the same as if you had pushed at the center.
 
  • #34
Yes that sounds credible, thanks FactChecker. Will now make up and work on some specific problems to see what happens.
 
  • #35
snoopies622 said:
Intuitively, it seems wrong to me that applying a (force x distance) to the edge of the pipe would result in the same linear kinetic energy as applying the same (force x distance) to the center of mass,...
Applying the same (force x time = impulse) will result in the same linear kinetic energy.
Applying the same (force x distance = work) will result in the same total kinetic energy.
 

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