Central Forces

Central force is the force that is radially pointing and the magnitude is dependent on the distance from the source. Examples of central forces are gravitational force, electrostatic forces, and spring force. In this article, let us learn in detail about the central force, its equation, examples and fields

What is Central Force?

The central force in classical mechanics is defined as the force that is acting on an object which is directed along the line joining the object and the origin. The magnitude of the central force depends only on the distance between the object and the centre.

Following are the theorems that relate central force with angular momentum:

Theorem 1: For an object to have its angular momentum conserved, the object should be subjected only to the central force.

Theorem 2: For an object to have its motion on a plane, the object should be subjected only to the central force.

Things to Remember 

• An object's angular momentum should be conserved if it is solely subjected to the central force.
• The magnitude of the central force is determined solely by the object's distance from the centre.
• When estimating the motion of the planets in the Solar System, the solution to the central-force issue frequently provides a decent first approximation of the true velocity.
• The magnitude of a central force can always be written as the derivative of a time-independent potential energy function if the central force is a conservative force.
• If the initial radius r and speed v satisfy the centripetal force equation, any central force can create uniform circular motion.
• The gravitational connection exemplifies classical activity, whereas the Coulomb interaction exemplifies quantum behaviour.