# Uniform Circular Motion

UNIFORM CIRCULAR MOTION

The movement of a body following a circular path is called a circular motion. Now, the motion of a body moving with constant speed along a circular path is called Uniform Circular Motion. The body has a fixed central point and remains equidistant from it at any given position.

If a particle is moving in a circle, it must have some acceleration acting towards the centre which is making it move around the centre. Since this acceleration is perpendicular to the velocity of a particle at every instant, it is only changing the direction of velocity and not magnitude and that’s why the motion is uniform circular motion. We call this acceleration centripetal acceleration (or radial acceleration), and the force acting towards the centre is called centripetal force.

Centripetal force is the force acting on a body in a circular path. It points towards the centre around which the body is moving.

### TIME PERIOD (T)

Time period (T) is the time taken by the particle to complete one revolution. It is denoted by ‘T’. If ‘r’ is the radius of the circle of motion, then in time ‘T’ our particle covers a distance = 2πr.

### FREQUENCY (F)

The number of revolutions our particle completes in one second is the frequency of revolution. We denote frequency by f and f = $\frac{1}{T}$. The unit of frequency is Hertz (Hz).

### ANGULAR SPEED

We measure this by measuring the rate at which the angle subtended at the centre changes. This quantity is ω and ω = Change in angle per unit time. Hence, ω is the Angular Speed.

The SI unit is radian / s or rad/s. For a single rotation, the change in angle is 2π and the time taken is ‘T’, therefore we can write:

ω = $\frac{2\pi }{T}$ = 2πν

CENTRIPETAL ACCELERATION

In the case of uniform circular motion, the acceleration is:

ar = $\frac{{V}^{2}}{r}$ = ω2r

If the mass of the particle is m, we can say from the second law of motion that:

F = ma

$\frac{m{v}^{2}}{r}$= mω2r

This is not a special force, actually force like tension or friction may be a cause of origination of centripetal force. When the vehicles turn on the roads, it is the frictional force between tyres and ground that provides the required centripetal force for turning.