# Circular Motion

Circular Motion

An object moving while rotating in a circle is referred to as being in circular motion. There are two types of circular motion: uniform and non-uniform. The angular rate of rotation and speed will remain constant in uniform circular motion, whereas the rate of rotation will fluctuate in non-uniform motion.

1. Uniform Circular Motion

If the magnitude of the velocity of the particle in circular motion remains constant, then it is called uniform circular motion.

2. Non-uniform Circular Motion

If the magnitude of the velocity of the body in circular motion is n constant, then it is called non-uniform circular motion.

Note A special kind of circular motion is when an object rotates around itself. This can be called spinning motion.

Variables in Circular Motion

(i) Angular Displacement Angular displacement is the angle subtended by the position vector at the centre of the circular path.

Angular displacement (Δθ) = (ΔS/r)

where Δs is the linear displacement and r is the radius. Its unit is radian.

(ii) Angular Velocity The time rate of change of angular displacement (Δθ) is called angular velocity.

Angular velocity (ω) = (Δθ/Δt)

Angular velocity is a vector quantity and its unit is rad/s.

Relation between linear velocity (v) and angular velocity (ω) is given by

v = rω

(iii) Angular Acceleration The time rate of change of angular velocity (dω) is called angular acceleration. Its unit is rad/s2 and dimensional formula is [T-2].

Relation between linear acceleration (a) and angular acceleration (α).

a = rα

Centripetal Acceleration

In circular motion, an acceleration acts on the body, whose direction is always towards the centre of the path. This acceleration is called centripetal acceleration. Centripetal acceleration is also called radial acceleration as it acts along radius of circle.

Its unit is in m/sand it is a vector quantity.

Centripetal Force

If a particles move with a uniform speed of V on any given circular path having the radius (r), the particle will have a centripetal acceleration of magnitude (v2/r). However, the direction continuously changes and always maintains its position towards the circle. We know according to the second law of Newton, the acceleration is produced by the force in the same direction as that of the force. It is that force which complex a body to move in a circular path.

Centripetal force is not something new. All the forces present in nature such as gravitational force, electrical force, frictional force, etc are centripetal forces. we can also say that a body undergoing circular motion occurs when a force acts upon it in the direction toward the centre of the circular path or the circle. This force is known as centripetal force. If the centripetal force is absent then the circular motion is not possible. Consider the mass of a body m and the magnitude of the centripetal force fcts centre.

For circular motion a centripetal force is required, which is not a new force but any force present there can act as centripetal force. where, m = mass of the body, c = linear velocity,

ω = angular velocity and r = radius.

Work done by the centripetal force is zero because the centripetal force and displacement are at right angles to each other.

Examples of some incidents and the cause of centripetal force involved.

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