Re: When Physical Intuition Fails

[Michael Bowen <fizzbowen@MINDSPRING.COM>]

At 07:37 2002/10/28, Oren Quist wrote:
> 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

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.