Angular displacement is the angle in degree or radian created by the circular motion of the object at the circumference of the circular path.
If an object covers d distance at the arc of the circle, it creates θ angle at its center and it relates to the formula:
d = rθ
Here, r = radius of the circle.
Also, θ = ωt
Where, ω = angular velocity
t = time taken.
After 12.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of +2.45 rad/s. During this time, the wheel has an angular acceleration of -7.5 rad/s2. Determine the angular displacement of the wheel.
Solution: Given that,
Angular velocity = 2.45 rad/s
Angular acceleration = 7.5 rad/s^2
Time = 12 sec
As we know that, in linear motion
d = vt + ½ at^2
We can use the same equation in circular motion,
θ = ωt + ½ αt^2
= (2.45)(12) + ½ (7.5)(12)^2
= 569.4 radians
A car is moving in circular track covers the whole track of distance 25m having radius of 5m from the center. Find its angular displacement.
We have given,
Displacement, d = 25 m
Radius of the circle, r = 5 m
So that, θ = d/r
= 25/5 = 5 radians.