This isn't a homework question, but it might as well be. The problem I have been pondering is:
If a disc (or children's roundabout if you like), of radius r, mass m, is spun around it's center with an initial force F, and thereafter there is the friction force (of either the axle or air resistance or both) of f, then how long will it take to come to a stop?
I have thought about it and have come up with not much. My first way is thus:
$F = ma$, so
$a = F/m$, the initial acceleration ( or should that be $(F-f)/m$ ?).
And then the deceleration is $a = -f/m$.
I'm not sure how to calculate the initial linear velocity, but assuming I have it, $u$, say, then I could say that after time $t$ the velocity is $v = u -at = u -ft/m$, where f is the friction force.
So then the disc would stop spinning when $ t= um/f$. I am aware that this is wrong (well, it might work if we were dealing with linear motion). Straight away it seems wrong because it doesn't take into account the radius of the disc and also the slow down seems linear, when from observation it seems rotating discs slow down and taper off to a standstill. But that is as far as I got. I have tried to use angular motion equations (well $\omega r = v$) but I am stuck at this point, and of course, finding the initial velocity.
Any help is appreciated.