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## Homework Statement

Please could someone help explain the case of a friction-less banked race track. If you take an Olympic indoor banked cycle track and imagine for a moment that it was friction-less. The laws of circular motion tell us that without friction the banked geometry can enable a cyclist to hypothetically still race round the track. The equation that tells us this is v = sqrt(rgtantheta) where v is the velocity of the bike, r is the radius of the track, g is gravity and theta is the angle of the bank. It says in my book that if you solve for a value of v for a friction-less track then the bike must ride at this velocity and this velocity only. Any less and it will slide down and any more and it will slide up.

My main question is, what keeps the bike from sliding on a friction-less surface if you maintain this speed? I understand that the vertical component of the reaction force counters the weight and the horizontal component provides the centripetal force. If you take the component of the weight acting down the slope then what counters this? I was thinking it might be the inertia of the bike but then inertia isn't strictly a force is it?

## Homework Equations

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v = sqrt(rgtantheta)