i.e.                    ∠AOB = ∠A′OB′

Adding              ∠AOB′ to both sides of the above relation, we get

                        ∠BOB′ = ∠AOA′ = θ (say)

This shows that in a given interval of time the angular displacements of all particles of the rigid objects undergoing rotation are identical.

Therefore, a single variable, viz. angular displacement (θ) may be used to define the rotational motion of the rigid object.

Angular velocity:

The power of change of angular displacement with respect to time is called as angular velocity.

Average angular velocity: The power of change of angular displacement with related to time is called as angular velocity.

To describe average angular velocity it is necessary to specify the interval in which we are talking for average. 

Instantaneous angular velocity: Concurrent velocity seems angular velocity at a particular instant. It is mathematically shown as ,       

Angular accelerations (ω):

The rate of change of angular velocity with related to time is called as angular acceleration.  

Average angular acceleration: It is important to denote the time interval to in which we are talking about average.

In a given time interval t₁ to t₂ the average angular acceleration is described as,

Instantaneous angular acceleration: Concurrent angular acceleration means angular acceleration at a particular dot instant at t = t₁ mathematically it is shown as,

Direction of angular acceleration: If value of ω increasing then direction of a will be equal as direction of ω and vice-versa.

Equation of angular motion:

            ω(t) = ω_o + at

            θ(t) = θ_o + ω_ot + 1/2αt²

             ω²_(t) = ω₀² +2αθ

Here    ω_o = magnitude of the initial angular velocity

            ω_(t) = value of the angular velocity after time t.

             _θo  =  Initial angular position.

            θ_(t) = Angular position after time t.

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