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Still when both linear and rotational movements are involved, even during the application of a force, I've always seen considering the body rotating around its center of mass, and in that case for what I know the linear force to which it’s subjected the center of mass is the same as the one applied, and the torque is equal to the force multiply the distance from the center of mass to the point of application of the force.

But if the point in translation is the pole then the linear force to which it’s subjected is still the same as the force applied?

For what I know it surely rotate around its center of mass only after the application of the force, but during it shouldn't. Is that right or wrong?