Rotation Mechanics about Unfixed Points

[jchodak2]

I was doing some rotation problems the other day out of my physics textbook when I realized that invariably all the problems dealt with rotation about fixed point (levers and pendulums and such). So I imagined a case in which I had a bar with a certain mass and dimension floating in space and I applied an impulse at some point on the bar (shot a bullet or a piece of gum, ellastic or inellastic, whatever), and I wanted to know how fast the bar would begin to translate compared to how fast it would rotate depending on where along the bar I applied the impulse (obvioulsy if I shot at it dead center it would translate only). I wasn't sure how to work this out and how I would employ the relevant kinematic equations for translation and rotation and linear vs angular momentum. This seems like an easy enough and straightforward problem, but I couldn't work it out and I found it interesting that my book had absolutely no problems of this kind. Can anyone help me?

 

[Feldoh]

This is a very interesting question. The first thing is that momentum is conserved so momentum of object doing the impulse = angular + translational.

Next thing is perhaps to figure out the moment of inertia and the length of the bar and then you'd be able to solve for one of the velocities from which you could figure out the other

 

[espen180]

Not pretending to be an expert, but I think this may be relevant.

When dealing with torque, there is general agreement that the magnitude of the torque is equal to the distance from the center of mass to the action point multiplied by the force component perpendicular to this line, or $$\vec{\tau}=\vec{r}\times \vec{F}$$. This is the part of the force contributing to rotational motion, so the component of the force parallel to $$\vec{r}$$ must contribute to translateral motion, right?

I haven't studied collisions that closely yet, but I should think that there is a similar way to deal with collision situation, though you will have to include conservation of angular and linear momentum.