Angular Displacement Calculator, Formula with Sample Examples

Angular Displacement Calculator :

Enter the angular displacement calculator, calculates the Distance travelled (s) in meters(m), Radius of the circular path (r) in meters(m), Angular displacement (θ) in radians(rad), and you get the calculator check it.

Angular Displacement Calculator

Angular Displacement Formula :

Angular Displacement = θf-θi The Displacement will have both magnitudes as well as the direction. The circular arrow pointing from the initial position to the final position will indicate the direction. It can either be clockwise or anticlockwise in direction.

θ=s/r, 

Where,

θ→ Angular Displacement,

s → distance traveled by the body, and

r →radius of the circle along which it is moving.

Simplistically, the distance traveled by an object around the circumference of a circle divided by its radius will be its Displacement.

Sample Examples :

Example1 :

Nena goes around a circular track that has a diameter of 4m. If she runs around the entire track for a distance of 80 m, what is her angular displacement?

Solution :

According to question Nena’s linear displacement s=80m

Also the diameter of the curved path d=4m

As we know that d=2r so r=4/2=2m

And according to the formula for angular displacement

Θ=s/r

Θ=80m/2m

Θ=40 radians

Example2 :

Rohit bought a pizza of a radius of 0.2 m. A fly lands on the pizza and walks around the edge for a distance of 90 cm. Calculate the angular displacement of the fly?

Solution :

According to the question, the distance traveled by the fly on the pizza is s = 90 cm = 0.09 m.

The radius of the pizza is given to be, r = 0.2 m.

Using the formula for angular displacement,

Θ=s/r

Θ=0.09/0.2m

Θ=0.018 radians

Leave a Comment