# Radial Acceleration

This article gives you important details of radial acceleration, which is one of the two components of angular acceleration, which helps in keeping an object in a circular motion.

Rohan Bhalerao

Last Updated: Jul 22, 2017

*a body of mass 'm' subject to a net force 'F', undergoes an acceleration 'a', that has the same direction as the force, and a magnitude that is directly proportional to the force and inversely proportional to the mass, thus, F = ma.*In other words, it gives us the simple definition, which is the rate of change of velocity with respect to time. This is true for linear motion, but what about the rate of change of velocity in circular motion?

Acceleration in Circular Motion

Radial Component

Radial acceleration 'a

_{r}' is the component of angular rate of change of velocity, whose direction is towards the center of the circle. This is also known as centripetal rate of change of velocity, which is present due to the centripetal force (directing towards the center of the circle), acting on the object. Mathematically, it is the square of velocity 'v' of the object, divided by the radius of the circle 'r'. So, its formula is a_{r}= v^{2}/r. It is actually the centripetal acceleration which is radially inwards. The units of measurement are denoted by radians per second squared or simply meters per second squared. Symbolically, it is written as ω/s^{2}or m/s^{2}.
Tangential Component

The component of angular acceleration tangential to the circular path is the tangential component. For instance, in a discus throw competition, when you fling the disc after one or two rotations, the disc travels along the tangential path of your hand's circular rotations due to the tangential component. Mathematically, it is a

_{t}= (v_{2}-v_{1})/t, where v_{2}and v_{1}are the respective velocities of the object in circular motion at two points measured over a time period t. Its unit of measurement is m/s^{2}.
Radial Acceleration of the Earth

_{re}= v

^{2}/r = (29800)

^{2}/149600000000 = 0.00593 m/s

^{2}. This is the value of the radial component which keeps us orbiting around the Sun.