Writing an equation for torque around an arbitrary point on a body

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Discussion Overview

The discussion revolves around the concept of torque in a rotating disc, specifically how to formulate the equation for torque about an arbitrary point on the rim of the disc. Participants explore the implications of this scenario on angular acceleration and the forces involved, considering both rotational motion and the frame of reference.

Discussion Character

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

Main Points Raised

  • One participant questions how to understand angular acceleration about an arbitrary point on the rim and whether a transition to that point's frame of reference is necessary.
  • Another participant suggests that an additional force must be considered at point O if the disc is not accelerating linearly.
  • Clarifications are made regarding the presence of a frictionless rod through point O, indicating that the disc is engaged solely in rotational motion.
  • It is noted that for a rigid body in a plane, the rotation rate of any point about any other point remains identical, implying that angular accelerations are also the same.
  • Participants discuss the necessity of including the force at point O, which balances the applied force F and contributes to the torque around point A.

Areas of Agreement / Disagreement

Participants express differing views on the forces acting on the disc and the implications for torque calculations. There is no consensus on the necessity of transitioning to the frame of reference of the arbitrary point or the exact nature of the forces involved.

Contextual Notes

The discussion includes assumptions about the nature of the forces acting on the disc and the conditions under which the torque is being analyzed, such as the presence of a frictionless rod and the fixed nature of point A. These assumptions may affect the interpretation of the torque equation.

Who May Find This Useful

This discussion may be useful for students and professionals interested in mechanics, particularly those studying rotational dynamics and torque in rigid bodies.

John Milton
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TL;DR
Writing an equation of torque around arbitrary point
Suppose there is a disc rotating around axis through its centre, with force F acting on the rim. The equation of torque is simple, however, what happens if it is written about an arbitrary point on the rim? How can the angular acceleration about that point be understood? Do I have to transition to its frame of reference?

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There must be an additional force about the point O if the disk is not also accelerating linearly.
 
Apologies, suppose there is a frictionless rod through the point O, so the disc is only engaged in rotational motion.
 
John Milton said:
Apologies, suppose there is a frictionless rod through the point O, so the disc is only engaged in rotational motion.
Frictionless rod or not, there is a force at O.
 
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John Milton said:
How can the angular acceleration about that point be understood?
For a rigid body in a plane, the rotation rate of any point about any other point is identical. The orientations of any lines you draw on the body will change in lock step.

If the rotation rates are the same, the angular accelerations are the same.

I assume that point A is fixed to the rotating body? And that we are referencing rotation rates against a non-rotating background?
 
jbriggs444 said:
For a rigid body in a plane, the rotation rate of any point about any other point is identical. The orientations of any lines you draw on the body will change in lock step.

If the rotation rates are the same, the angular accelerations are the same.

I assume that point A is fixed to the rotating body? And that we are referencing rotation rates against a non-rotating background?
Thank you for the reply. Yes, the point is fixed, and the background is not rotating
 
John Milton said:
Thank you for the reply. Yes, the point is fixed, and the background is not rotating
As @PeroK noted, you need to include the foce at O, which balances F and also contributes to the torque around A.
 
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