Analysis of Centripetal and Centrifugal Forces

The definition of centrifugal force, according to, is “An outward force on a body rotating about an axis, assumed equal and opposite to the centripetal force and postulated to account for the phenomena seen by an observer in the rotating body.” It defines centripetal force as “The force, acting upon a body moving along a curved path, that is directed toward the center of curvature of the path and constrains the body to the path.”

Uniform circular motion happens when the motion of an object is constant around a circle. The centripetal acceleration is directed toward the center of the circle, causes the object to change direction, but does not change the speed of the object. It acts at right angles to the velocity. The centripetal force directed toward the center of the circle at right angles to the velocity causes the object to move. The centripetal force is the net force that causes the circular motion.  In circular motion, centripetal force and centripetal acceleration are directed toward the center of the circle. Velocity is on a tangent to the path of the circle and perpendicular centripetal acceleration. Centripetal acceleration and centripetal force are parallel.

The formula for the centripetal force is f=ma=mv^2/r, where f is the centripetal force, m is the mass of the object and a is the centripetal acceleration in the first equation. In the second equation, m is the mass of the object, v is the tangential velocity and r is the radius of curvature of the circle.

The centripetal force of a planet orbiting its sun is gravity. This gravitational force is directed toward the center of mass of each object. For circular orbits, it is the center of the circle. For non-circular orbits, only the component of the gravitational force that is orthogonal to the center of the osculating circle is defined as the centripetal force. The remaining force causes the object to speed up and slow down.

Centrifugal force is caused by the inertia of the object as the object continuously changes direction around the circle. Inertia means if the object is at rest it stays at rest unless it is acted upon by an outside force. It is a reaction force caused by the centripetal force. The reactive centrifugal force is the reaction force to the centripetal force of the object in uniform circular motion. The object constantly accelerates toward the axis of rotation.

The centripetal force is exerted from another object, causing the centripetal acceleration. The reactive centrifugal force is the force that causes the centripetal force from the other object. According to Newton’s Third Law of Rotation, the force exerted is equal and opposite.