# Linear acceleration caused by a force applied outside the center of mass

I´m trying to figure out, how does Newton's first law work when the force is applied outside the center of mass. Does it have any effect on the object's linear acceleration (not rotational)? If it does, how do I calculate it?

• Hi! Here is a possible duplicate of your question physics.stackexchange.com/q/66960 – DelCrosB Oct 8 '16 at 21:08
• What are your thoughts on this? Do you have any hypothesis? – Sanya Oct 8 '16 at 23:14

There is no difference on the motion of the center of mass (and thus the whole "linear" motion of the body) if the force is not applied directly to it, but somewhere else on that rigid body. The internal forces cancel exactly and thus all external forces will generate the acceleration, regardless of their point of action. See my related question here: click.

Imagine that a force $\vec F$ is applied to a body.
The line of action of this force does not pass through the centre of mass $C$ of the body.

Apply two forces $\vec F_1$ and $\vec F_2$ at the centre of mass of the body such that $\vec F = \vec F_2$ and $\vec F_1 + \vec F_2 =0$ as shown in the diagram below.

Uou now have a force $\vec F_2 (= \vec F)$ acting along a line through the centre of mass of the body which will only produce a translational acceleration of the body and a couple consisting of the two forces $\vec F$ and $\vec F_1$ of magnitude $Fd$ which will only produce a rotational acceleration of the body.