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I was recently instructed by my instructor that the axis of rotation in the case of a couple always passes through the center of mass and is parallel to torque,Why is this true?

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2 Answers 2

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In mechanics, a couple refers to two parallel forces that are equal in magnitude, opposite in sense and do not share a line of action.

A better term is force couple or pure moment. Its effect is to create rotation without translation or, more generally, without any acceleration of the centre of mass.

Your one statement is correct that the axis of rotation is parallel to the torque but it passes through center of mass is not always correct.

enter image description here

In the diagram above, a couple is applied to a disk of diameter $D$. That is, a force $F$ is applied to opposite sides of the disk. The torque do to the couple is: $$τ=F×d_1+F×d_2$$ where $d_1$ and $d_2$ are the distance to some (arbitrary) point $O$.

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  • $\begingroup$ Could you provide an example for the same? good read tho $\endgroup$
    – user245838
    May 19, 2020 at 9:05
  • $\begingroup$ Example for what?? $\endgroup$
    – SarGe
    May 19, 2020 at 9:06
  • $\begingroup$ that axis may not pass through com $\endgroup$
    – user245838
    May 19, 2020 at 9:08
  • $\begingroup$ The axis passes through the point where the object is hinged. If it is not hinged, the axis passes through center of mass. $\endgroup$
    – SarGe
    May 19, 2020 at 9:15
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For any couple, the axis of rotation is always through the COM and is truly parallel to the torque. Torque is a vector whose direction is determined by the right hand rule. Depending on the orientation, the torque can be pointing either up/down or into/out of the reference plane. And this direction will always be parallel to the rotation axis. To understand why an object including a couple would rotate about this point, you must remember that rotation also has it's own inertia. Every point/axis is not created equal when it comes to rotation. This implies that any axis at all has it's own inertia (how easily you can rotate the object about the axis). It turns out objects have least inertia for rotation about their COM . For this reason, an object would naturally prefer to rotate about this point than any other point since it is easier for them. Except rotation is forced about any other axis, every object would tend to swing about this unique point. You may as well consider the parallel axis theorem $I_p=I_{cm}+Md^2$ and the implication for this explanation. Good luck!

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  • $\begingroup$ The direction of torque is given by the right hand rule and the statement that the rotation axis is parallel to torque is correct. $\endgroup$
    – ModCon
    May 19, 2020 at 5:59
  • $\begingroup$ @ModCon I admit. I just thought about it. $\endgroup$ May 19, 2020 at 6:39
  • $\begingroup$ Could it be said by the right hand thumb rule that the direction of movement of palm w.r.t the thumb is actually w.r.t . the axis( which passes through the thumb)? $\endgroup$
    – user245838
    May 19, 2020 at 9:07
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    $\begingroup$ @JoeSantino Yes! It is correct to imagine the direction the thumb points as the rotation axis. Remember the thumb points in the direction of the torque which we have said is also parallel (same direction) as the axis of rotation. So yes! $\endgroup$ May 19, 2020 at 9:31
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    $\begingroup$ But @Joe Santino's question says that it always passes through COM, which is wrong. $\endgroup$
    – SarGe
    May 21, 2020 at 11:17

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