A wind turbine blade has a point 5 m from the hub. If that point moves with a linear speed of 20 m/s, what is the angular velocity of the turbine?

What the problem is asking

You are given a linear (tangential) speed of a point on a rotating blade and its distance from the hub (the radius). From that, you can find the blade’s angular velocity.

Use the tangential speed relationship

For circular motion, tangential speed $v$ and angular velocity $\omega$ are related by: $$v = r\omega$$

Solve for angular velocity

Rearrange to isolate $\omega$: $$\omega = \frac{v}{r}$$ Substitute $v = 20\ \text{m/s}$ and $r = 5\ \text{m}$: $$\omega = \frac{20}{5} = 4\ \text{rad/s}$$

Quick check

Units work out because $\text{m/s} \div \text{m} = 1/\text{s}$, which matches $\text{rad/s}$ (radians are unitless).