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Angular Displacement Formula

Angular displacement formula with solved examples: Explore more about the Angular displacement formula with solved examples.

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

faq

Frequently asked questions

Get answers to the most common queries related to the Angular Displacement Formula.

What is the need to use angular displacement?

Ans. The angular displacement is used to calculate the position of an object that moves around the circumference of ...Read full

Will the displacement be negative?

Ans. The displacement depends on the direction and magnitude, so it’s a vector quantity. Thus, displacement can sh...Read full