Here are some examples of circular motion – an artificial satellite orbiting the earth at a constant height; a stone which is tied to a rope and is being swung in circles, a car is turning through a curve on a race track.

When the motion of an object in a circle is at a constant speed, it is called uniform circular motion. An object that moves in a circle is constantly changing its direction. This means that an object that is forming a circle on a path along with that particular object will complete repeated strips around the path in the same amount of period at every time. For instance, the object is moving at a tangent to the circle.

Below are some examples of uniform circular motion:

The changes that take place in the direction are accounted by radial acceleration which is given by the given equation.

a

Changes that take place in the speed have implications for radial acceleration. There may be two possibilities that are as follows:

Below are the examples of non-uniform circular motion:

In the above mention examples, the speed is varying.

Variable of

The angle which is made by the position vector with the given line is called angular position. Two dimensional motion or motion in a plane is a circular motion.

For instance- Suppose a particle P is moving in a circle having radius r and centre O. The position of the object P at a given instant may be expressed by the angle q between OP and OX. This q angle is called angular position of the particle. As the object moves in the circle its angular position q change.

An angle rotated by a position vector of the moving object in the mentioned time interval with some reference line is called angular displacement.

Important points of angular displacement:

w = total angle of rotation/ total time taken

Therefore; θ

Where, θ

The rate at which the position vector of a particle with respect to the centre rotates, it is called instantaneous angular velocity with respect to the centre.

w = Δ θ/ Δt = dθ/dt

Important points:

Where, t = period and f = frequency of uniform circular motion

W

Where θ = a – bt + ct

Angular velocity is described with respect of the point from which the position vector of the moving object is drawn. The angular velocity of the particle w.r.t ‘O’ and ‘A’ will be different here. It is mentioned as below:

W

Therefore, w

In two perpendicular directions, Newton’s law is applied in a circular motion. The first direction is along with the tangent and the other direction is perpendicular to it (towards the centre). The component of force acting along the tangent is called the tangential (Ft) and the component of force acting at the mid is called the centripetal force (Fc).

Tangential force F

Centripetal force F

Note: If the centripetal force is absent, the object will move in a straight line with constant speed.

Instantaneous circle (R) has radius of:

R = [1+ (dy/dx)