Answer: [tex]7.958 \frac{rad}{s}[/tex]
Step-by-step explanation:
We are told the wind turbine makes 76 revolutions in 1 minute. This means the angular speed [tex]\omega[/tex] of the object in revolutions per minute (rpm) is:
[tex]\omega=76 rpm=76 \frac{rev}{min}[/tex] (1)
However, we have to convert this to [tex]\frac{rad}{s}[/tex], since this is the unit used in the International Systme of Units for angular speed.
So, we can do this knowing that:
[tex]\omega=\frac{2 \pi}{T}[/tex] (2)
Where:
[tex]2 \pi=360\°[/tex] is the value of one revolution
[tex]T=1 min=60 s[/tex] is the period of rotation
With this information in mind, let's make the conversion:
[tex]\omega=76 \frac{rev}{min}. \frac{1 min}{60 s}. \frac{2 \pi}{1 rev}[/tex] (3)
[tex]\omega=7.958 \frac{rad}{s}[/tex] (4) This is the wind turbine angular speed
