When an impulsive force is acted upon a rigid body, (and the force doesn't pass through the centre of mass) why does the body rotates specifically about an axis passing through centre of mass ?
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An impulsive force directed along a line crossing the center of mass doesn't produce a torque relative to this center. It causes only a linear momentum change, i.e., a translational movement and no rotation of the body. Any other impulsive force on the body produces a torque relative to the center of mass causing an angular acceleration of the body around the center of mass (and a linear acceleration). This results in a constant angular momentum, i.e., a constant rotation of the body around an axis through the center of mass after the impulsive force has ended. A free floating rotating body always rotates around an axis going through its center of mass.
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