Rotational Motion Clarification

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Discussion Overview

The discussion revolves around the dynamics of a ball attached to a massless rod, specifically focusing on the moment of inertia and the forces required for acceleration. Participants explore the implications of the ball's rotation about its own axis while being fixed to the rod.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion regarding the moment of inertia for a ball attached to a rod, suggesting it should be calculated as mr², similar to a free ball.
  • Another participant agrees that the ball rotates around its own axis and posits that this rotation implies a greater force is needed for the same rate of acceleration.
  • A later reply introduces a more detailed calculation for the moment of inertia, suggesting that it should include both the ball's inertia and the rod's contribution, represented as I = I_{ball} + mL².
  • One participant mentions that their instructor and textbook provide a different perspective, indicating a potential disagreement with established views.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are competing views regarding the calculation of moment of inertia and the implications for force required for acceleration.

Contextual Notes

There are unresolved assumptions regarding the simplifications made in the moment of inertia calculations and the conditions under which these approximations hold true.

Moose352
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I got a little confused thinking about this. Consider a ball attatched to a (massless) rod. This system is to be accelerate about the free end of the rod. From what I know, the moment of inertia for this system would simply be the mr^2, since this is the same case as a free ball being accelerated at the same rate. However, it seems to me that the ball is also rotating around its own axis (since it is fixed on the rod), and thus wouldn't the force necessary for the same rate of acceleration be greater?
 
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Is this question too dumb for anyone to even answer? :wink:
 
Originally posted by Moose352
Is this question too dumb for anyone to even answer? :wink:
No, it's an excellent question.

Originally posted by Moose352
However, it seems to me that the ball is also rotating around its own axis (since it is fixed on the rod), and thus wouldn't the force necessary for the same rate of acceleration be greater?
I would say that the answer is yes. Using I = mL2 (L is length of stick) is just an approximation: it assumes the radius of the ball can be neglected.

A more realistic value for rotational inertia must include that of the ball as well:

[tex]I = I_{ball} + mL^2 = \frac{2}{5}mR^2 + mL^2[/tex]
 
Thanks Doc. My physics instructor (and the book) was saying otherwise and wouldn't concede to my view.
 

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