Concept Test 1
A biology teacher and a physics teacher 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 of them skidded and fell off the cliff. Who?
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.
Concept Test 2
A biology teacher and a physics teacher (of similar mass) took the chair swing ride at the amusement park. The bio teacher chose an outer chair (B) while the physics teacher chose an inner chair (A). Unfortunately, the motor went berserk, and the ride reached an unreasonably high speed. A cable snapped and a teacher went projectile though the air. Which one?
The bio teacher went projectile (tangentially btw).
The bio teacher chose an outside chair, the bike accident still fresh in the memory presumably. Alas, at the SAME ANGULAR VELOCITY, the outer path with the larger radius of turn requires a larger centripetal force. (Think Fc=mrω2) The tension (the horizontal component, to be specific) in the cable, which provides the required centripetal force, is thus always larger for the outer chair than the inner chair. Logically, the outer cable should snap first.
P.S. It is misleading to think Fc=mv2/r because the two motions do not have the same linear speed v.