Angular Displacement, Angular Velocity and Angular Acceleration | Physics Grade XI

Circular Motion

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Angular Displacement, Angular Velocity and Angular Acceleration | Physics Grade XI

Angular Displacement, Angular Velocity and Angular Acceleration

Angular displacement
The angular displacement of the object moving in a circular direction is defined as the angle traced out by the radius vector at the center of the circular path in a given time. The SI-unit of angular displacement is radian.

Angular velocity
The time rate of angular displacement is called angular velocity and is denoted by ω.
 
Mathematically, ωav = angular displacement / time interval
                             = (θ2 – θ1)/(t2 – t1)
                             = ∆θ/∆t
 
Time period
The period of an object in circular motion is defined as the time taken to complete one revolution. It is denoted by T. since in time T, the object completes one revolution i.e. an angle of 2π radians, angular velocity of an object is
     ω = 2π/T
 
Frequency
The number of revolutions completed per second by an object in circular motion is called frequency and is denoted by f. the relation between the frequency, f and period, T is
     F = 1/T
Therefore, we have
The unit of frequency is hertz, Hz.
 
Angular acceleration
The rate of change of angular velocity with respect to time is called angular acceleration. It is denoted by α.
     .: Angular acceleration, α = Change in angular velocity/time taken
 
If ω0 and ω are the initial and final angular velocities and t is the time taken to change the angular velocity, then,
     α = (ω – ω0)/ t
     ω = ω0 + α. T
 
Angular acceleration is measured in radian per second square (rad. s-2) and its dimensional formula is [M0L0T-2].
    Angular acceleration is also given by, dω/dt

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