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I'm not a physicist and just making some research by the way of creating simple physics simulator, because of that, sorry if this is very dumb question, but I really need help with it.

Let's assume that some body (rectangle, square, N-polygon, etc.), exists in 2D world in rest (no friction, gravity, etc.) and can be freely moved in any direction.

If some pushing / pulling force will be applied to center of mass, then only translational force will exist, this case is very clear to me. But what if force will be applied on the edge of body? What will be if force will be applied at some angle to edge? I understand that this will involve a rotational forces. But how can I calculate the resulting translational vector in this case?

Here is image, demonstrating the problem. Force F2 will not involve any rotational forces, I can calculate net force (= F2) and get acceleration vector. All this question is about F and finding resulting translational vector after apply of F.

example of forces-related question

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    $\begingroup$ I'm not physician You won't find many physicians here :-P $\endgroup$ – jinawee Dec 3 '13 at 20:17
  • $\begingroup$ Applying the forces will cause a linear acceleration and an angular acceleration. The linear acceleration will always be the sum of the forces divided by the mass. If you want to know the angular acceleration, you should change your question to reflect that. $\endgroup$ – Brian Moths Dec 3 '13 at 20:37
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The translational accelleration will be the force divided by the mass.

The cross product of the force vector with the vector from the touch point to the center of mass is the torque applied to the object.

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  • $\begingroup$ I think your first version with dot product is exact answer! $\endgroup$ – TSB99X Dec 3 '13 at 21:43
  • $\begingroup$ @Tony: No, that dot product comment was wrong, which is why I deleted it. Fortunately I realized the mistake within the time window of editing a post for free, so no record of the mistake remains. If you are looking at translation only (just the movement of the center of mass point), then it doesn't matter where the force is applied on the object. The center of mass accellerates F/m. If the force is off center, there will be some torque too, but the translation will be the same either way. Draw a free body diagram if you don't believe. $\endgroup$ – Olin Lathrop Dec 3 '13 at 23:14

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