Complex-ish physics/maths question on the speed a car would need to take to go around a loop.

Complex-ish physics/maths question on the speed a car would need to take to go around a loop.
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answer:The acceleration of circular motion is ( v ^2 / r ) where v = speed and r = radius of track. Because the track is vertical, the acceleration at the top must exceed the acceleration due to gravity. Otherwise the car falls off the track. So the critical velocity is given by: v^2 / r = g where g = gravitational acceleration. So v^2 = g * r, and v = sq.root (g * r). As long as v is greater than this value the loop-the-loop is safely executed. The car is always falling due to gravity. The trick is to go fast enough so the track is pushing downward on the car harder than gravity is pulling downward. From the viewpoint of the driver, centrifugal force at the apex exceeds gravity.
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