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Uniform Circular Motion

Circular motion: A point is moving in such a way that it keeps a contant distance from a fixed point, such motion is known as circular motion. 

P is the position of object.

O is the center which fixed point. 

s is the linear displacement. 

θ is the angular displacement. 

t is the taken time in s displacement. 

Angular displacement: The angle swept out by its radius vector in the given  time interval. 

Angular velocity: The rate of change of angular velocity of a particle with respect to time is called its angular velocity. Which is denoted by Omega (ω).

According to rule of θ 

 θ = x/r 

x = r . θ

Linear velocity (v) = x/t 

Angular velocity (ω) = θ/t

Unit of angular velocity = radian/second or radian s^-2

instantinious velocity (ω) = 

Time period: The time taken by a particle to complete one revolution along its circular path is called its period of revolution. It is denoted by Capital T and measured in second. 

Frequency : The frequency of an object in a circular motion is define as the number of revolution completed in per unit time (one second). It is denoted by nu (v). 

Relation between angular velocity (ω),  frequency (v) and time period (T) :

According to difinition of time period, a particle copmpletes one revolution in time T. Which traverses an angle of 2π radian in T second. 

angular displacement =  2π radian

Angular velocity (ω) = θ/t = 2π/T 

in term of nu (v) 

 (ω) = 2 πv