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I have a rigid body with an origin point (at the center of mass).

I want to apply a force on a certain point.

So what is the force applied to the origin of this rigid body?

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Note: I don't want the moment of torque.

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Assume $p$ is a point in the space of a rigid body.

So if we had a force $\vec F_{p}$ at a point $p$, how can we get the $\vec F_{center}$?

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Any force applied to any part of a rigid object acts on the object as a whole. So if you were to place a directional force meter at the center of the object (or at any other point on the object), it would register the force $\vec{F}_p$.

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  • $\begingroup$ but if it wasn't in the center , it will cause a torque . how does the energy still the same as if without torque ? $\endgroup$
    – MhdSyrwan
    Nov 4, 2011 at 17:27
  • $\begingroup$ Because the rotation imparted by the force means that it takes more work to push the body obliquely. $\endgroup$
    – Ron Maimon
    Nov 4, 2011 at 19:33
  • $\begingroup$ could you explain more please ? $\endgroup$
    – MhdSyrwan
    Nov 4, 2011 at 23:24

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