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Suppose you have a disk in a vacuum that is completely unconstrained (not fixed at its center). If you apply a tangential force at a point on the circumference of the disk, does the force act purely as a torque and begin to change the angular momentum of the disk without changing its linear momentum? Or does the disk center also accelerate forward through space?

I am split between the scenarios since, on the one hand, a force at a point on the circumference is transferred by the rigid disk to the center, thus accelerating it. But there is also a torque on the body, which changes angular momentum. Can someone explain?

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You will have both rotational and translational acceleration since there is a net force acting on the disc. Therefore you will have both angular and linear momentum.

If you had two equal but opposite forces acting on opposite sides of the diameter of the disc (a force couple) then you would have pure rotation.

Hope this helps

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