A biology teacher and a physics teacher (of similar mass) were riding bikes at the SAME SPEED when they approached a bend. The bio teacher took the inside track (A) while the physics teacher took the outside track (B). One teacher skidded and slid down the cliff. Which one?
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The bio teacher skidded.
The bio teacher chose the inside track (A), presumably thinking that it is safer to stay away from the cliff. Alas, at the SAME SPEED, the inside track with the smaller radius of turn requires a larger centripetal force. (Think Fc=mv2/r) Skidding occurs when friction (between the tyre and the road) is not large enough to provide the required centripetal force.
P.S. It is misleading to think Fc=mrω2 because the two motions do not have the same angular velocity ω.