# Force accelerates center of mass same regardless of where applied?

1. Jun 1, 2014

### EkajArmstro

Is it true that the center of mass of an object will be accelerated with the same direction and magnitude from the same force no matter if the force is applied to the center of the object or to the edge of the object?

I have heard some people say this is not true because some of the "force" will be used up as torque in making the object spin.

However, from what I remember of high school physics the original statement is true. As far as intuitively understanding this I can picture it being because the side you are pushing is accelerated more but the far side is accelerated less and it averages out to the same center of mass movement.

Sorry if this makes no sense :) Thanks to anyone who can help!

2. Jun 1, 2014

### Matterwave

You will always have F=ma, no matter where the force on a rigid body is applied (a will then be the center of mass acceleration). Of course, this assumes that you know all the F's (including constraint forces, e.g. normal forces).

3. Jun 1, 2014

### Delta²

This is true (it doesnt matter if the same force also creates Torque). However your intuitive understanding is abit wrong. It is better to read the proof of this statement in a standard textbook. The proof make use of the 2nd and 3rd newton laws of motion and of the definition of the center of mass. The key to understand the proof is that the sum of all the internal forces between the various infinitesimal portions of the rigid body is always zero at all times, and that is a consequence of newtons 3rd law.