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so this is the question that's been bothering me:

Say you have a simple rigid body in space that is at rest or travelling with only translational motion at a constant speed. Say that the body is something like a rod and it's not rotating. So, at some point, an external force is acted on the rod, just for an instance and it is not acted on some axes that goes through the center of mass. What will happen??

My guess is that it will start rotating about the center of mass (because of torque) + it will get some translational motion towards the direction of the force. Is that correct? and if so, how much of the force becomes rotation and how much translational movement and why??

please forgive my english and thnx in advance!!

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Dear gkostra Welcome to Physics SE. Your english is impeccable, I shouldn't have know that it wasn't your mother tongue (it's mine) if you wouldn't have said so. – WetSavannaAnimal aka Rod Vance Aug 1 '13 at 23:53
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The answer to this question is as simple as you seem to think it is. Let's consider the case of two spatial dimensions for simplicity. Let's take our object to be moving inertially without rotation, and we choose a frame co-moving with the object. Additionally, lets choose our origin to be at the center of mass of the object.

Now suppose we apply an impulse $\mathbf{J}$. If the mass of the object is $m$, Newton's laws tell us the final center of mass velocity of the object must be $\mathbf{J}/m$. This tells us the translational part.

Next we consider the rotation. We know the angular impulse will depend on the place where the force is applied to the object. If the force is applied a position $\mathbf{r}$ and the object has moment of inertia $I$, then the angular impulse $K$ will be $\mathbf{r} \wedge \mathbf{J}$. (The wedge is basically a cross product). The resulting angular velocity about the center of mass is then $K/I$.

Your last question makes me think your intuition isn't that good. You say how much of the force becomes rotation and how much becomes translation. It doesn't work like that. All of the force goes into translation and all of the force goes into rotation. If you had a fixed amount of impulse you could generate and wanted to make a bigger rotational speed, you wouldn't have to sacrifice translational speed. In fact, you couldn't sacrifice translational speed---it will always be $J/m$. The only way you could get more rotational speed is by using a bigger lever arm, which doesn't affect the translational speed.

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Many many thnx! your answer couldn't be more helpful!! – gkosfra Aug 2 '13 at 8:44

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