How about looking at upper and lower bounds of some kind?
If you draw pictures of the velocity vectors, it is pretty easy to see that if it is spinning quickly most frictional work goes into slowing the spin, while if it is translating quickly most frictional work goes into slowing the...
I did make a bit of progress today. If you consider a translating+spinning object and another identical object that is only translating with the same velocity but not spinning, the two objects start with the same translational energy and the frictional forces doing the work of stopping the...
I don't have time right now for a full response, but this is incorrect. The pieces fly off in straight lines, but those straight lines don't intersect the center of mass.
While I completely respect the prevailing attitude on PF, I consider this thread a special case because:
1) I have done very little real physics in decades unless you include arguing with the wife about the efficacy of cheap diswashing detergent vs. expensive dishwashing detergent.
2) Along...
So can somebody give a complete answer without making reference to other posts in the thread? I'm sorry, but I still don't see a full solution here. :(
Right. I should have known it was too easy. It's been a few decades since I've done any real physics!
And right again. I kept thinking about the force being opposite to the velocity, so I had "opposite" on my tongue.
How about this?
The frictional force on each point is opposite to the direction of that point's velocity.
So (by Newton's Third Law) the deceleration on each point is opposite to the direction of that point's velocity.
But that point's velocity can be written as a sum of a...
Yes, the two limiting cases are excluded. You just sort of fling the book across the suface so that it both translates and rotates. Maybe somebody has the book (big and green with yellow waves as I recall) and can give us the exact wording.
It is supposed to be a 'qualitative' problem, so I don't think they wanted you to write much. Something like gralla's argument may be on the right track. Berkeman, the high spin case exception you mention is probably because the surfaces are not perfectly flat. Anyway, it is not my question...
Yes, very catchy title. But it also happens to be true! Here's the windup: This question comes from the Halliday and Resnick edition that was used in the 80's. I was a grad student at the time at a very prestigious department and somehow this question came to my attention. I couldn't figure...
I thought I would do a little physics for fun, since it has been over 20 years since I last did any. I picked up Sethna's Stat Mech book. He gives a derivation of the diffusion equation that goes as follows:
A particle makes random steps, ie x(t+Δt)=x(t) + l(t). The steps l(t) are given...