Find centripetal acceleration and force for an object moving in a circle.
An object moving in a circle at constant speed is still accelerating, because its direction is constantly changing. This centripetal acceleration points toward the centre of the circle and has magnitude a = v²/r. A real force must supply this acceleration, given by F = mv²/r.
The centripetal force is not a new kind of force; it is whatever real force points toward the centre, such as tension, friction, gravity, or the normal force. For a car turning a corner it is friction; for a satellite it is gravity. Enter the mass, speed, and radius to find both the acceleration and the required force.
Centrifugal force is a fictitious force that appears only in a rotating reference frame. In an inertial frame the real, inward centripetal force is what keeps the object on its circular path.
Force scales inversely with radius. A smaller radius at the same speed means a larger acceleration and therefore a larger required force.