Centripetal acceleration is also involved in roller coasters, and explains the experience of a rider in a roller coaster while it moves in a circular motion. It is not a true force, but rather the result of an object’s inertia, or resistance to change in direction, as the object moves in a circular path. The "force" points toward the center of the circle, but a roller coaster rider would feel centripetal acceleration as a force pushing them toward the outer edge of the car.
Centripetal acceleration is given by ar = v2/r where ar 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.
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