A roller coaster car of mass m moves with a speed v through a circular loop-the-loop of radius r. What is the minimum speed the car must have at the top of the loop to maintain contact with the track?

Core Concept

At the minimum speed, the normal force from the track becomes zero, and the only force acting on the car is gravity. For circular motion, the centripetal force is provided by gravity: mg = mv²/r. Solving for v, we get v = √(gr).