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I made up this problem, on two ends of an uniform stick AB there acts two parallel & like forces of $15N$ and $35N$(on A and B respectively). So there is resultant force of 50 N and it acts on point P which is $15/35$ m away from B.

As the resultant force doesn't work on the COM, the stick will spin.

The problem is how to measure the torque in this case. There seems to be no fixed axis relative to which the stick is spinning.

Any hint on this regard?

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There is a standard technique for dealing with this.
You apply two forces at the centre of mass which are opposite in direction but equal in magnitude to the original force.
You are then left with a force whose line of action is through the centre of mass and a couple whose torque is independent is the same about any point.

enter image description here

The second diagram is to show you how you can deal with more than one force.

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  • $\begingroup$ Isn't rotational axis will be the midpoint between the couple? $\endgroup$ – Mockingbird Nov 1 '16 at 12:56
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    $\begingroup$ A couple is a very interesting arrangements of forces. To test what I written work out the torque due to couple about point $A$ and then about point $B$ and then any other ointment on the digram which is not on line $AB$. You should get $500$ Nm clockwise at every point. $\endgroup$ – Farcher Nov 1 '16 at 12:59

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