Expert: Daniel Mazur - 8/4/2009

Question
Hi Daniel,

Hope you had a nice vacation.

I wanted to still discuss the rotation model that i gave previously.

Suppose we have our plank again and it's free to rotate.
Now I push it at some point with a force F.

Now we had previously discussed that this force is applied by me on a particular region of the plank and this particular region then transmits the force along the entire plank due to the presence of electromagnetic bonds.

My question is that how is this force distributed to the entire plank? Does the magnitude of the force transmitted fall off with the distance from the point where I applied the force?
Or is it that this same force, F, that I applied is transmitted to each and every atom of the plank?

If thesecond option is correct, then we have a contradiction, because if every constituent particle experiences the same force F forward, that has been transmitted to it by neighboring particles, and assuming all the constituent particles have same mass, the entire plank should move forward with the same acceleration instead of rotating..??

Please correct me....

Thanks,
Shikhin


Answer
Hi Shikhin,

the experimental fact is that the plank starts to rotate, hence the force F acting in a point at a distance x, x.neq.0, from COM, is not "propagated" to other points as a constant. Like I told you before, to get the correct total effect of a force F on a plank you do this: consider force F at COM PLUS a moment of force-pair M=F*x. Put this into an equation of motion and solve for any point of the plank at vector R=(rx,ry,rz) from COM and there will be your answer.

It has nothing to do with principles anymore, it's just calculus. You need to be very careful in setting up the system of coordinates and the initial conditions of the eq. of motion. I recommend that you first consider whether or not your force F is time independent (magnitude AND direction) or time dependent (direction, with constant magnitude). These two have VERY different solutions!

My apologies for taking too long to respond - we had a situation at work after I came back from holidays that didn't let me concentrate on anything else.

Good luck with the maths.

Daniel