Moment of Inertia of multiple bodies in contact

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Discussion Overview

The discussion focuses on the moment of inertia of multiple cylinders in contact, specifically regarding how they behave when subjected to torque. The context includes theoretical considerations of rotational dynamics and the application of formulas related to moment of inertia.

Discussion Character

  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant inquires about the overall moment of inertia of multiple cylinders in contact, specifically when rotated about an axis through their center of mass.
  • Another participant suggests that while the usual formula can be applied, understanding the reaction to torque on a single wheel may require considering the simple sum of the individual moments.
  • A participant confirms interest in how the entire setup reacts to torque and questions whether the moment of inertia of the whole assembly would indeed be the sum of the individual parts.
  • It is noted that if the axes are fixed and torque is applied to a single wheel, the moment of inertia can be evaluated around that axis.

Areas of Agreement / Disagreement

Participants appear to agree on the approach to calculating the moment of inertia for the setup when considering fixed axes and torque applied to a single wheel. However, the discussion does not resolve whether this method is universally applicable in all scenarios.

Contextual Notes

The discussion does not address potential limitations or assumptions regarding the configuration of the cylinders or the nature of the torque applied.

Jeremymu1195
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What is the overall moment of inertia of many cylinders in contact, where each is rotated about an axis through its center of mass. For example, a set of rollers. (See picture)
 

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You can apply the usual formula, but if you want to know how they react to torque on a single wheel (instead of torque on the whole setup), you are probably interested in the simple sum of the individual moments.
 
Yes, I am interested in how the whole setup reacts to a torque. So the moment of inertia of the whole assembly would be the sum of the moments of the individual parts?
 
If those axes are fixed and you apply torque to a single wheel (evaluated around its axis), yes.
 
Cool, thank you!
 

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