# Angular Velocity and Angular Acceleration

## Angular Velocity:

The rate of angular displacement of a particle with time is called the angular velocity of that particle.

So, Angular Velocity = Angular Displacement / time

Angular velocity is expressed by the symbol ω.

While revolving in a circular path, if a particle subtends equal angles at the centre in equal intervals of time, the particle is said to be in uniform circular motion.

During a uniform circular motion, if a particle subtends an angle θ at the centre in time t, then the angular velocity of the particle will be ω = θ/t

If the circular motion isn’t uniform, then the total angle subtended θ divided by the total time t is called the average angular velocity of the particle.

So, average angular velocity, ω = θ/t

### Instantaneous Angular Velocity:

The Instantaneous Angular Velocity of a particle at a given point is the limiting value of the rate of the angular displacement, from that point concerning a time interval when the time interval tends to zero.

### Unit and Dimension of Angular Velocity:

Usually, the unit of angular displacement is radian, hence the unit of angular velocity = (unit of angular displacement/unit of time)

Since angular displacement is a dimensional quantity.

Dimension of angular velocity = (dimension of angular displacement / dimension of time) = 1/T = T-1

## Angular Acceleration:

The rate of change of angular velocity of a particle with time is called the angular acceleration of that particle.

Let us consider a particle under rotational motion whose initial velocity is ω1 and final angular velocity after time t is ω2. So, according to the definition,

Angular Acceleration (α) = change in angular velocity / time
= (ω2 – ω1) / t

### Instantaneous Angular Acceleration:

The Instantaneous Angular Acceleration of a particle at a given point is the limiting value of the rate of the change in velocity concerning a time interval when the time interval tends to zero.

### Unit and Dimension of Angular Velocity:

Unit of angular acceleration = radian / second2

Dimension of angular acceleration = dimension of angular velocity/dimension of time
= T-1 / T = T-2