# Equations of motion

## Main Question or Discussion Point

Say, I have a system at rest. I was wondering - how many equations of motion can the system have (without redundancy)? Well, I thought that equating the forces along 2 or 3 different axes would give 3 independent equations. Also equating torques would give some equations, but how many of them (independent) can I formulate? Kindly help me.

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haruspex
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Say, I have a system at rest. I was wondering - how many equations of motion can the system have (without redundancy)? Well, I thought that equating the forces along 2 or 3 different axes would give 3 independent equations. Also equating torques would give some equations, but how many of them (independent) can I formulate? Kindly help me.
Assuming you mean a rigid body in equilibrium, count the potential accelerations. In 3D, the mass centre has three degrees of freedom for linear accelerations. That leaves rotational acceleration about the mass centre. In 3D, there are two degrees of freedom for the orientation of the net torque.

But it does not have to be three linear force equations and two torque. There are other ways of getting five independent equations in 3D. E.g. in 2D, instead of two linear and one torque you could have one linear and two torque, provided the two torque axes do not lie on a line parallel to the linear force equation.

Edit: I should have written "... do not lie on a line normal to the linear force equation".

Last edited:
• Thejas15101998
But it does not have to be three linear force equations and two torque. There are other ways of getting five independent equations in 3D. E.g. in 2D, instead of two linear and one torque you could have one linear and two torque, provided the two torque axes do not lie on a line parallel to the linear force equation.
Could you please give me an example? And moreover, If two torque equations (considered from two different points on the plane say in case of 2D) are such that the torques are parallel to each other then does that always imply redundancy or not?
Thank You

haruspex