Centripetal force

The centripetal force is the force that acts on an object to keep it moving in a circular path. The magnitude of the centripetal force for an object with mass m moving on a circular path (with radius r) at a constant tangential velocity v is given by Fc=mv2/rthe equation where centripetal force is equal to mass times velocity squared, divided by radius of the circular path..

A black circle with a green ball placed on its edge, indicating movement in a circular path. The ball has a mass of m, and the distance r from the centre of the circle. The velocity of a moving ball is visualized by a horizontal arrow coming from the ball to the left, and marked by letter v. The centripetal force is visualized by a vertical arrow coming from the centre of the ball towards the centre of a circle. On the right from the circle, the equation for the force is given as mass multiplied by velocity square, divided by the distance.

Figure 1: Schematic of circular movement of an object with mass m

It can be useful to write the centripetal force in terms of angular velocity ωwith a symbol of lowercase omega, which is equal to velocity multiplied by the radius of the path, so that Fc=mrω2centripetal force is equal to mass times radius times angular velocity squared. The orbital period is given by T= 2π/ωperiod being equal to 2 times pi divided by angular velocity, so the centripetal force can be expressed as Fc=mr(2π/T)2centripetal force equal to mass times radius times 2 pi divided by orbital period squared.
The centripetal acceleration (following Newton's second law of motion) is given by v2/r velocity squared divided by the radius and radially directed towards the center of the circular path.
As follows from Fc=mr(2π/T)2the equation for centripetal force being equal to the mass times radius times 2 pi divided by orbital period squared, the centripetal acceleration of e.g. a satellite can be calculated when the radius and the period T are given. Knowing the distance of the moon from the earth and the time it takes the moon for one round-trip, Newton calculated the centripetal acceleration of the moon from which he deduced the inverse square law of gravitation.