Question

If a wind turbine makes 76 full revolutions every 1 minute what is it’s angular speed?

Answer 1

Answer: $7.958 \frac{rad}{s}$

Step-by-step explanation:

We are told the wind turbine makes 76 revolutions in 1 minute. This means the angular speed $\omega$ of the object in revolutions per minute (rpm) is:

$\omega=76 rpm=76 \frac{rev}{min}$ (1)

However, we have to convert this to $\frac{rad}{s}$, since this is the unit used in the International Systme of Units for angular speed.

So, we can do this knowing that:

$\omega=\frac{2 \pi}{T}$  (2)

Where:

$2 \pi=360\°$ is the value of one revolution

$T=1 min=60 s$ is the period of rotation

With this information in mind, let's make the conversion:

$\omega=76 \frac{rev}{min}. \frac{1 min}{60 s}. \frac{2 \pi}{1 rev}$ (3)

$\omega=7.958 \frac{rad}{s}$ (4) This is the wind turbine angular speed