# Law of Motion XV

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Time Period of Uniform Circular Motion: Total time taken by the particle performing uniform circular motion to complete one full circular path is known as time period.
In one time period total angle rotated by the particle is 2π and time period is T.
Hence angular velocity
Frequency: Number of revolutions made by the particle moving on circular path in one second is known as frequency.
Centripetal Acceleration: When a body performs uniform circular motion its speed remains constant but velocity continuously changes due to change of direction. Hence a body is continuously accelerated and the acceleration experienced by the body is known as centripetal acceleration (that is the acceleration directed towards the center).
Consider a particle performing uniform circular motion with speed v. When the particle changes its position from P1 to Pits velocity changes from 1 to Pis ∆v which is directed towards the center of the circular path according to triangle law of subtraction of vectors.
due to change of direction. The change in velocity from P From figure ∆OP1Pand ∆ABC are similar, hence applying the condition of similarity

Since the change of velocity is directed towards the center of the circular path, the acceleration responsible for the change in velocity is also directed towards center of circular path and hence it is known as centripetal acceleration.

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