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So, we studied in classical mechanics that every action has an equal and opposite reaction. So if we apply a force to some object, that object will exert an equal amount of force on us but in the opposite direction.

Can the same also be said about torques? If so, can someone explain how it could be possible?

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  • $\begingroup$ The tags Qmechanic put on the question were better than what you put on, so I have rolled back to the previous tag edit. If the current answers do not sufficiently answer your question, please leave comments on the answers explaining why. If there is an answer that is sufficient for you, please mark it as the accepted answer for future readers. Also, make sure to upvote any answers you find to be useful (even if they are not the accepted answer). $\endgroup$ Commented Aug 4, 2019 at 3:50

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Something to keep in mind: torques are not as fundamental as forces. I say this for two reasons. First, torques are defined in terms of forces. Second, the torque produced by a force depends on our subjective point of reference. With that being said, if you have confusions about torques, the best place to start is to just think about forces instead.

So let's do that. Let's say I apply a tangential force of magnitude $F$ to the edge of a wheel of radius $R$ with my hand. Well then by Newton's third law the wheel applies a force to my hand of equal magnitude and opposite direction as the force I applied to the wheel. Both forces act at the same point in space: the point of contact between my hand and the wheel.

Let's look at the torque of these forces about some point, say the center of the wheel. Then the torque of my force is $$\tau_{\text{me}}=FR$$ and by Newton's third law the torque of the wheel's force is $$\tau_{\text w}=-FR=-\tau_{\text {me}}$$ So we do in fact get an "equal but opposite torque".

It is worth pointing out that just like for forces this does not mean both torques act on the wheel. My torque acts on the wheel. The wheel's torque acts on me.

I'll also point out that just like how Newton's third law for forces gives us linear momentum conservation, this version of the third law for torques gives us angular momentum conservation.

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A torque is exactly the same as two equal and opposite forces acting at different points on a body.

Each force has an equal and opposite reaction force, and the reaction forces are the same as an equal and opposite torque.

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  • $\begingroup$ You can have a torque from a single force. The OP isn't asking about the specific case of a pure torque produced by two equal but opposite forces. $\endgroup$ Commented Aug 4, 2019 at 3:57
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Yes, but the opposite reaction torque is not always useful.

If you defined torque as $\tau = r \times F$, then the force $F$ always follows Newton's third law. For any contact force, $r$ is the same. Since $r \times (-F) = -(r \times F)$, it follows that the "third law force" delivers a "third law torque".

For non-contact forces, $r$ is different, but the math will always work out. Otherwise, angular momentum would not be conserved for the closed system of both objects.

All of that said, this "third law torque" can be deceptive. The original torque is defined with respect to some axis - wherever $r$ is measured from. Unless you are interested in how both of the interacting objects are rotating around the same axis, the interaction torque is useless. If you are unsure, you can always find the underlying force and use that third law pair.

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