# Angular Speed

## Angular Speed

Angular speed is the rate at which an object changes its angle in radians, in a given time period. Angular speed has a magnitude only.

$$Angular\,\,Speed\,\,=\,\,\frac{\left( Final\,\,Angle\,\,-\,\,Initial\,\,Angle \right)}{time}\,\,=\,\,\frac{Change\,\,in\,\,position}{time}$$

Angular Speed (ω) = θ/ t

Where,

ω = Angular Speed in rad/sec,

t = time in seconds.

Angular speed and angular velocity uses the same formula. The difference between the two is that Angular speed is a scalar quantity, while angular velocity is a vector quantity.

How to find the Angular Speed?

Problem: At the state fair, you take your younger sister to ride the Ferris wheel. You notice that a sign says that the angular speed of the Ferris wheel is 0.13 rad/sec. How many revolutions will the wheel complete in 12 minutes?

Solution: Given,

Angular speed (ω) = 0.13 rad/ sec

Time (t) = 12 min = 720 sec

We know that:

Angular Speed (ω) = θ/ t

θ = ω x t = (0.13 rad/ sec) x 720 sec = 93.6 rad.

θ = 93.6/ 2π revolutions = 14.9 ≈ 15 revolutions.

∴ θ = 15 revolutions.