# Angular Displacement Formula

The angular displacement is defined as the angle through which an object moves on a circular path. It is the angle, in radians, between the initial and final positions.

(θ_{f} - θ_{i}) = angular displacement

θ = s/r

θ = angular displacement through which movement has occurred

s = distance travelled

r = radius of the circle

Angular Displacement Formula Questions:

1) A runner goes around a circular track that has a diameter of 8.5 m. If he runs around the entire track for a distance of 60 m, what is his angular displacement?

Answer: The linear displacement of the runner, s = 60 m. The diameter of the curved path, d = 8.5 m = 2r, so r = 4.25 m. Solve the equation for θ.

θ = s/r

θ = 60m /4.25 m

θ = 14.12 radians

2) The bakery of a small Indiana town has just made a huge strawberry shortcake for the opening of the summer festival. The cake has a radius of 0.5 m. A ladybug lands on the cake and walks around the edge for a distance of 80 cm. What is the angular displacement of the ladybug?

Answer: The distance travelled by the ladybug, s = 80 cm = 0.08 m. The radius, r = 0.5 m.

θ = s/r

θ = 0.08m/0.5 m

θ = 0.16 radians

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