## Angular displacement formula

The angle at which an object moves on a circular path is called angular displacement. It is expressed with a symbol of theta (θ). It is measured in radians or in angles. If an object creates an angle from the centre of the circle to any point in a rotational motion, then the object shows the angular displacement.

The formula given down below is the way to find out the angular displacement.

**Angular Displacement (θ) = Distance travelled (s)/Radius of the circular path (r)**

S= length of the arc

R= radius of the circle

Θ= angular displacement

## Let us take some examples on Angular displacement:

**Example 1:** A boy runs about 400 meters around a circular track. 35 meters is the radius of the track. What will be the angular displacement?

**Solution:**

Given:

Distance Travelled (s) = 400 meters

The radius of the circular track is 35 meters

Angular Displacement = The Distance Travelled / Radius of Circular Path

Substituting the given value in the formula = 400 / 35

= 11.42 radians

Therefore, the angular displacement will be (θ) = 11.42 radians

**Example 2:** A circular track with a diameter of 7 m is where Julie goes for a jog. She runs for about a 50m distance around the entire track, to find the angular displacement?

**Solution: **

Given:

As per the question,

Julie’s linear displacement, s = 50 meters

Also, the diameter of the circular track = is 7 meters

And we know,

d = 2r, so r =7/2= 3.5 m

Now, as per the formula for angular displacement,

θ = 50m /3.5 m

θ = 14.28 radians