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Friction and rolling on a ramp



Today we were discussing the rolling of a hoop down a ramp. The discussion
led to a comparison of the friction when the hoop is lying on its side
(does not roll) to when it does roll.

The friction in both cases is,I believe, of the static variety ( less than
or equal to mu* mgcosT where T = theta). When on its side as there is no
acceleration the friction is equal to mgsinT. When on a roll, it drops
(for a hoop) to mgsinT/2.

I think there is something magical and mysterious about how it is that
friction adjusts with the same mu and normal to be different in the two
circumstances. To quote my favorite Thermos joke, "How does it know?" The
friction becomes what it needs to be for each situation. Yet,the mechanism
of it escapes me.

Any thoughts?

Ken Fox
Science Department Coordinator
IB Physics Teacher
Smoky Hill High School
Aurora, CO
kfox@mail.ccsd.k12.co.us