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?
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?
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