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CURVILINEAR MOTION

The motion of a body along a circular path is known as circular motion, the centre of rotation remains fixed. The examples of the bodies moving in a circular path are: shafts, flywheels, pulleys etc., rotating about their geometric axis.

5.6.1. Angular Velocity. It is defined as the rate of change of angular displacement of
a body. Angular displacement is always measured in terms of angle covered by the body from the initial position.

Let a body is moving along a circular path as shown in Fig. 5.11. Let initially the body is at A and after time ‘t’, the body is at E. Let AOB = Θ.

Then angular displacement = AOB =Θ

Time taken = t.

Angular velocity

5.6.2. Relation Between Linear Velocity and Angular Velocity. Consider the body
moving in a circle as shown in Fig. 5.11. The initial position of the body is at A and after time ‘t’ the body is at B. The angle AOB is equal to θ.

Where ω = Angular velocity

5.6.3. AngularAcceleration. It is defined as the rate of change of angular velocity. It is measured in radians per second per second and written as rad/s2. Mathematically, angular acceleration (α) is given as

α = Rate of change of angular velocity