explain how centre of mass help the system to move as well as rotate
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The interesting thing about the center of mass of an object or system is that it is the point where any uniform force on the object acts. ... If we push on a rigid object at its center of mass, then the object will always move as if it is a point mass. It will not rotate about any axis, regardless of its actual shape.
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in most cases moment of inertial about center of mass is the least and that's why the body rotates about the center of mass.
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