Is Torque Equal on All Axes When a Rigid Body's Net Force Is Zero?

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SUMMARY

The discussion confirms that when the net force on a rigid body is zero, the torque about any line perpendicular to the plane of the forces is indeed equal. The key equation involved is τ = Iα, where τ represents torque, I is the moment of inertia, and α is angular acceleration. The participants assert that since angular acceleration (α) remains constant across all axes for a rigid body, the moment of inertia (I) must also be equal for all axes, leading to the conclusion that torque is uniform. This conclusion is derived from the properties of rigid body dynamics and the nature of cross-products in torque calculations.

PREREQUISITES
  • Understanding of rigid body dynamics
  • Familiarity with the equation τ = Iα
  • Knowledge of angular velocity and angular acceleration
  • Basic concepts of torque and cross-products
NEXT STEPS
  • Study the implications of the parallel axis theorem in rigid body dynamics
  • Explore the relationship between torque and angular momentum
  • Learn about the conditions for static equilibrium in rigid bodies
  • Investigate the effects of varying moment of inertia on rotational motion
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone studying mechanics, particularly those focusing on rigid body dynamics and rotational motion principles.

miss photon
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Homework Statement


prove that when the net force on a rigid body is zero, the torque about any line perpendicular to the plane of the forces is equal.


Homework Equations


[tex]\tau[/tex]=I[tex]\alpha[/tex]


The Attempt at a Solution


it is known that angular velocity, and hence angular acceleration about any line is the same for a given rotating rigid body.
implies, [tex]\alpha[/tex] is same about all lines.
if we accept the above statement to be true, then I comes out to be equal about every axis, which is a contradiction.
 
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If it's perpendicular the the cross-product will just be tau = |r||F|
 
Last edited:

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