How is centripetal force defined mathematically?

The mathematical definition of centripetal force is expressed as Fc = mv^2/r, where Fc represents the centripetal force acting on an object moving in a circular path, m is the mass of the object, v is the tangential velocity, and r is the radius of the circular path.

Centripetal force is essential for keeping an object moving in a circular trajectory, as it is always directed towards the center of the circle. The formula illustrates that the force required to maintain circular motion increases with both the mass of the object and the square of its tangential speed, while it inversely depends on the radius of the circular path. Thus, for an increase in either mass or velocity, a greater centripetal force is required to sustain circular motion, while a larger radius allows for relatively less force.

Other equations presented concern different physical principles, such as torque, linear motion, and displacement, which do not apply to centripetal motion and consequently do not define centripetal force.