Torque on a fixed reference of falling masses

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Discussion Overview

The discussion revolves around a thought experiment involving two falling masses and the concept of torque in relation to angular acceleration. Participants explore the relationship between torque, moment of inertia, and angular acceleration in the context of free-falling objects.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant describes a scenario with two masses in free fall and calculates torque based on their distances from a fixed point, leading to a comparison of angular accelerations.
  • Another participant questions the expectation of angular acceleration being greater for the mass producing greater torque, prompting a discussion about the relationship between torque and angular acceleration.
  • A later reply acknowledges the importance of considering moment of inertia in the relationship between torque and angular acceleration, suggesting that this was a missing element in the initial reasoning.

Areas of Agreement / Disagreement

Participants appear to agree on the need to consider moment of inertia in the context of torque and angular acceleration, but there is no consensus on the initial expectations regarding the relationship between torque and angular acceleration.

Contextual Notes

The discussion highlights the dependency on the moment of inertia in the torque-angular acceleration relationship, which was not initially considered by the first participant.

FG_313
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I had a little thought experiment, in which there are two objects with the same masses near each other (same height) on freefall. If I set up a point that is on an instant besides the two masses and call it the center of torque, I get that the torque produced by the nearest one's weight is T=F.d, where d is the distance to the imaginary point. The other one is T'=Fd', where d'>d and F=mg. I find that the torque T'>T and so I expect a'>a, where a is angular acceleration. But for a small instant of time, the geometry of the problem will tell you that the angle of the first mass made with the point (call it o) is larger than the angle the other one is making, because they are falling on the same rate. And so o'<o and a'>a. That for me is very difficult to understand why... Am I missing something? Thanks in advance!
 
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FG_313 said:
I find that the torque T'>T and so I expect a'>a, where a is angular acceleration.
Hi FG_313, welcome to PF!

Why do you expect that? What is the formula relating torque and angular acceleration? Does it involve any other quantity?
 
Thanks for the quick answer, don't know why I missed something like that. If the moment of inertia is considered the result makes sense.
 

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