Re: kinetic energy paradox?

["Carl E. Mungan" <mungan@USNA.EDU>]

>  > nitpicker's note: Consider a wheel on your car rolling along pavement
> >  at constant speed on a flat road. Suddenly you hit an icy patch. But
> >  you don't panic. You keep the wheel straight and you keep your feet
> >  off the accelerator and brakes. Doesn't the wheel keep rolling
> >  merrily along?
> Yes, but only because it was rolling before it hit the icy patch,
> right? A wheel placed on a truly frictionless horizontal surface
> can't roll can it?

True enough for a wheel without a drive shaft. But if there is a
drive shaft attached to the wheel, I can craftily apply just the
right pressure on the gas and brake pedals to keep the wheel spinning
on ice in such a way that it always matches the rolling without
slipping condition.

You would probably protest that not's really rolling. But how about
the following then: if I have a spool (with a suitable moment of
inertia) and I pull on the thread at just the right angle, I can get
the spool to roll (starting from rest) even on a frictionless surface
(without slipping), can I not? (Sorry I couldn't resist bringing this
up ;-)

Which is to say, friction is not really required for rolling. Nor is
it true that if I apply a force to an object to get it to move on an
arbitrarily rough surface that the friction must oppose the motion.
The friction could be zero or even in the direction of motion. I tell
the students I'll demo this. I then walk towards them and tell them
the demo is over.
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/