| Chronology | Current Month | Current Thread | Current Date |
| [Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
[ Oren Quist ]
>I don't understand why this problem is so "misleading."
> Unless of course I have done it all wrong!
> By simple methods I get the final velocity to be
>
> Vf = (IR) / (I+ MR^2) x wo
>
>Which has the final velocity independent of the frictional
coefficient.
I was lazy and assumed that the wheel was a uniform
cylinder or disk (I = 0.5MR^2).
With this assumption, I obtained the pleasingly simple
result V_f = (1/3)Rw_0. This is consistent with Oren's
more general formula above, when my specific I is
plugged in, and was also obtained using simple
(non-calculus) methods (basically, N2 and its extension
to rotational motion). The result is again independent
of mu, but I am still having trouble reconciling this to
the case mu = 0, which clearly has different
behavior.
I am thinking it might be instructive to analyze the
behavior in the limit as mu approaches zero; the
amount of time required for the wheel to stop
slipping will obviously increase asymptotically.
Also, I haven't figured out how the rolling distance
needed to achieve non-slippage changes
with mu, but it shouldn't be difficult to do.
The behaviors in the limit as mu approaches
infinity (velcro, anyone?) might also be instructive.
--MB