Box with a horizontal force at the top

[chandran]

Theory says that a cubical box when subjected to a force horizontally(not at the centre of gravity) then the force will tend to rotate the box around the centre of gravity. Any proof can be given for this?

 

[Doc Al]

This is a consequence of Newton's laws of motion. The off-center force, assuming it's the only force acting, does two things:
(1) It accelerates the center of mass
(2) It exerts a torque about the center of mass, producing an angular acceleration

 

[chandran]

docal,
that is where i am asking. Why don't the box rotate about some other point. why it should rotate about cg. Any mathematical proof?

thanks.

 

[Doc Al]

I think I see what the issue is. Since torque can be found with respect to any point, then any point can be considered as an "axis of rotation". This is true. But for any point other than the center of mass you will be mixing up the translation with the rotation. So using the center of mass is for convenience in describing the motion: the motion of an object is the sum of the translation of its center of mass plus the rotation about the center of mass.

Note that this does not mean that the object is in pure rotation about the center of mass! The instantaneous axis of rotation (the point about which the object appears to be in pure rotation) can be anywhere.