<P> where a is centripetal acceleration, v is velocity and r is the radius of the circular path . This shows that two roller coaster cars entering two loops of different size at the same speed will experience different acceleration forces: the car in the tighter loop will feel greater acceleration while the car in the wider loop will feel less acceleration . </P> <P> Instead, the car is pulled to the top of the first hill and released, at which point it rolls freely along the track without any external mechanical assistance for the remainder of the ride . The purpose of the ascent of the first hill is to build up potential energy that will then be converted to kinetic energy as the ride progresses . The initial hill, or the lift hill, is the tallest in the entire ride . As the train is pulled to the top, it gains potential energy, as explained by the equation for potential energy below: </P> <P> U g = m g h (\ displaystyle U_ (g) = mgh) </P> <P> where U is potential energy, m is mass, g is acceleration due to gravity and h is height above the ground . Two trains of identical mass at different heights will therefore have different potential energies: the train at a greater height will have more potential energy than a train at a lower height . This means that the potential energy for the roller coaster system is greatest at the highest point on the track, or the top of the lift hill . As the roller coaster train begins its descent from the lift hill, the stored potential energy converts to kinetic energy, or energy of motion . The faster the train moves, the more kinetic energy the train gains, as shown by the equation for kinetic energy: </P>

When does a roller coaster train have the highest potential energy