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Is this true:

  1. When force is applied to a sphere NOT on center of mass (COM) then the sphere will move the same way as when force is ON center of mass, because the sphere is symmetric in every direction. So the kinetic energy is the same in both cases?

  2. But since the force is NOT on COM, the sphere will be rotated, so the sphere has both kinetic and rotation energy. So the sphere receives more energy when the force is NOT applied on COM?

I think that energy must be the same in both cases, but I don't know where does it go wrong?

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Energy is force times distance. You haven't specified a distance, so you can't say how much energy that force delivers.

If you allow the force to rotate the sphere, the application point will accelerate faster than it would if the sphere does not rotate. So a constant force will deliver energy to the sphere faster than it would in the non-rotating case.

But "faster" is not "more" unless you want to specify that the force must be delivered for a fixed amount of time.

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It is not true that the same force has to create the same change in kinetic energy. For instance, if two equal forces of opposite directions are applied on a body, the body does not change its energy. Thus each force makes zero work, or zero change in kinetic energy. You could tell that both forces create kinetic energies in different directions and that they cancel each other. But this cannot be true because kinetic energy can only be positive.

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