# Centripetal Force

An excerpt from the book: "An Introduction to the Physics of Sports" by Dr Vassilios M Spathopoulos.

According to Newton, in order for the velocity of a body to change, a force must be exerted on it. This applies both to the magnitude of the velocity and its direction. When a body performs circular motion its direction is constantly changing and so is the direction of its linear velocity that is always perpendicular to the radius of the circle. This is the reason that the discus always starts its flight at a direction perpendicular to the arm of the athlete.

The force responsible for the change in the direction of a body in turning motion is called the centripetal force and always has a direction towards the center of the circular path. The centripetal force is not an independent force in the way as forces such as weight, air resistance, etc., may be considered. In order for circular motion to be possible, some resultant force must be acting on the body with a direction always to the center of the circle. This resultant force will play the role of the centripetal force, whose magnitude is given by,

Fc = m Ω2 R

Where m is the body mass,
Ω is the angular speed
R is the radius of the circle.

In the case of discus throwing for example, the force that acts as the centripetal force is that exerted by the hand of the thrower onto the discus. The hand is constantly turning (until the throw) so the force it exerts on the discus fulfils the aforementioned direction requirements. A similar situation occurs when a cyclist racing in a velodrome (arena for track cycling) takes a tight turn. Velodromes have track inclinations that may be higher than 45 degrees. This design helps to provide the forces acting on the athlete with the necessary direction to become centripetal.