When a body moves in a circle, its motion is called as Circular Motion. When a body moves in a circular motion with a constant speed then this type of motion is called as **Uniform Circular Motion**. Consider different points lying on the blade of a ceiling fan as shown in the figure. If the fan rotates, then all such points will rotate together in circular motion with the same angular velocity which is denoted by ω (read as omega). This angular velocity is time dependent.

When at t = 0, the fan is switched on then its angular velocity i.e., ω = 0. , Initially the angular rotation covered is very small for an infinitesimal time interval\( t_1\)

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In the figure shown below, the points A,B,C and D have equal angular displacement for a given time. The path covered by them is circular with different radius but the angular velocity is same for every point on the fan at any instant of time.

In case of uniform circular motion, the speed is constant but velocity is changing every instant. If an object is moving in circular motion then it will also have an acceleration acting towards the centre due to which the object rotates about the centre. However, as this acceleration acts perpendicular to the velocity, it just alters the direction of the velocity, while its magnitude remains constant and, therefore, such an object is in uniform circular motion. This acceleration is centripetal acceleration (or radial acceleration), and the force acting

towards the centre is called centripetal force. In case of uniform circular motion, the acceleration is:

\(a_r~=~\frac{v^2}{r}~=~ω^2 r\)

Since, F = ma

F = \(m \frac{v^2}{r} = m~ω^2r \)

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

So if an object is moving in uniform circular motion:

- Its speed is constant
- Velocity is changing at every instant
- There is no tangential Acceleration
- Radial (centripetal) acceleration = \(ω^2\)
rr - v = rω

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