Angular Velocity and Angular Acceleration:
The angular velocity of a body in a fixed circular motion is the angle swept out by the radius vector per second. If the radius vector goes out an angle ΔΘ in a time interval Δt, the angular velocity is shown by
where is expressed in rad s-1. Simple velocity (v), angular velocity (ω) and the radius (r) of the circular motion are related as
v = ωr
Radian measure of an angle: If the arc of a circle similar as the radius, then the angle subtended by that arc at the centre of the circle is called a radian; it is similar to about 57.3o.
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Angular Acceleration: The angular acceleration α is given by ,
Linear acceleration (a), angular acceleration (α) and radius (r) of the circular motion are correlated as a = rα Angular acceleration is defined in rad s-2.
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Centripetal Acceleration:
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If a body goes in a circle at a constant velocity, it is said to be in uniform circular motion. In such type of motion, the magnitude of the velocity is fixed but the direction of the velocity vector is continually modifying. Thus the velocity is modifying with time. Hence the motion of the body is accelerated. The acceleration is tends towards the center of the circle and is known centripetal acceleration. The value of the centripetal acceleration is shown by ac =ωv
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where is the angular speed and is the velocity along the circle. Since v = ωr , we have, 
where r is the radius of the given circular path. The angular frequency is based on time period T and frequency v as, 
Therefore, centripetal acceleration is also define by (since 
) ,
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UNIFORM CIRCULAR MOTION
(i) Velocity remains fixed in magnitude but changes in direction
(ii) The acceleration is always simple to the velocity vector.
(iii) The acceleration is usually directed tends to the centre of the circular path.
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Comparison of uniform circular motion with projectile motion and straight line motion:
NON-UNIFORM CIRCULAR MOTION
(i) The velocity modifies both in magnitude as well as in direction
(ii) The velocity vector is usually tangential to the path
(iii) The acceleration vector is not in the opposite direction the velocity vector
(iv) The acceleration vector has two elements
(a) Tangential acceleration at modifies the magnitude of velocity vector,i.e. at = dv/dt
(b) Normal acceleration or centripetal acceleration ac modifies the direction of the velocity vector, i.e. ac=v2/r
(v) The complete acceleration is the vector sum of the centripetal and tangential acceleration 
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