What is the difference between the center of mass and center of gravity of a rigid body?
In which cases are they the same point and in which cases are they different points?
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For all practical purposes they are the same thing but say you had like a non uniform gravitational field, then the center of mass is not the center of gravity. Center of gravity can be considered as the point where torques due to the different forces of the gravitational field vanishes.
See this wiki article for more information: https://en.wikipedia.org/wiki/Center_of_mass#Center_of_gravity