A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.

Explanation:

Let the radius of the loop be r. When the rider is upside-down, only gravitational acceleration g = 9.81 m/s2 and centripetal acceleration a acting in opposite direction to keep you balanced. Therefore

a = g

So the minimum speed must be so the rider does not fall our of the car

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