Force applied at centre of mass

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chandran
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If a force is applied at centre of mass the object will only translate and not rotate. Can anyone proove this mathematically?
 
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Torque is the cross product of the vector from the center of mass to the point where the force is applied (r), and the force. If r is zero, or r is parallel to the force, there will be no torque, and so no rotational force.
 

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