centre of mass and center of gravity
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The center of mass is the mean position of the mass in an object. Then there's the center of gravity, which is the point where gravity appears to act. For many objects, these two points are in exactly the same place. But they're only the same when the gravitational field is uniform across an object.
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Centre of mass is the point at which the distribution of mass is equal in all directions, and does not depend on gravitational field.
Centre of gravity is the point at which the distribution of weight is equal in all directions, and does depend on gravitational field.
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