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I have read two very similar yet conflicting threads on this site involving a pure torque applied to one end of a floating body in free space (no air resistance).

Torque applied off the center of mass - This answer says if a pure torque is applied to one end offset from the center of mass, the body will simply rotate around the center of mass without the motion of the COM changing.

However,

Reaction of applying a torque on a rigid body in space - In this question I asked earlier, the answer to nearly the same question is that the motion of the COM will change due to a pure torque.

So, which one is it? (I suspect my confusion might be an improper definition of a pure torque?) Note: Assume the rod is initially at rest in space and the frame of reference is a stationary observer.

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  • $\begingroup$ Hi Jonathan, you may enjoy this lecture of the Royal Institution all about spinning and rotation. I've added a timestamp for a pure torque demo, but honestly the entire lecture is great. $\endgroup$ Commented Apr 20, 2020 at 14:19
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    $\begingroup$ In the link to your second question you did not specify an applied torque on the end of the rod, but rather an applied force. An applied torque has no net force associated with it. Both answers you linked to are correct for the associated question posed. The comment in the first link is incorrect or misleading. A pure torque/couple does have a point of application, but the moment due to that couple about any point in space is simply the couple itself. $\endgroup$ Commented Apr 20, 2020 at 14:20

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The second question there (yours) isn't about a situation where there is "pure torque".

You only have one force acting on the object, so it creates a torque and moves the centre of mass because there is a net force. A "pure torque" requires a "force couple" where the two forces cancel out on the centre of mass as $0$ net force; but due to the direction of the forces, it still produces a net torque on the object, which causes rotation without translation (A.K.A. pure torque, pure moment, or pure rotation).

Another interesting thing about a pure torque is that the moment is independent on the point you are measuring torque about; which is a special feature of pure torque. If you apply a pure torque, the moment vector at one end would be the same as the moment vector of the centre of mass, which is an interesting result not typical of non-pure moments.

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  • $\begingroup$ Thank you for clearing that up. So a "pure torque" is not at all the same thing as a force applied perpendicularly. That explains it. $\endgroup$ Commented Apr 20, 2020 at 14:27
  • $\begingroup$ @JonathanLemon I think you will find this is consistent with the answer I gave you on similar question. $\endgroup$
    – Bob D
    Commented Apr 20, 2020 at 16:23

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