Question

The output frequency of the wind turbine is \[50Hz\]. What is meant by this statement?

Answer 1

Hint: The output frequency is the output produced by the wind turbine. So it represents the speed of the turbine or rotor in the turbine. This means that the frequency of voltage generated by the wind turbine is \[50Hz\] even if the wind is of fluctuating form The term speed means how fast or slows an object moves. Similarly, angular speed tells us how fast or slow an object rotates. It is as simple as that. In other words, it can be defined as the change in the angle of the object per unit of time. The angular speed is usually used to describe the speed of the rotational motion. The angular speed is measured in radians.

Complete answer:
We know that the angular speed determines the rate at which an object changes its angles which is measured in radians in a given time. As for how the speed is a magnitude, angular speed is also a magnitude. The formula for the angular speed is as follows.
\[\omega = \dfrac{\theta }{t}\]
Over here, \[\omega \] refers to the angular speed in radians/sec
$\theta $ refers to the angle in radians. (\[2\pi radians\] = \[ 360degrees\])
\[t\] Refers to the time in seconds.
We can also write the angular speed formula as,
\[\omega = 2\pi f\]
Over here \[2\pi \]represents the angle.
\[f\]Represents the frequency (\[f = \dfrac{1}{t}\])
From the question, if we substitute for \[f\]=\[50Hz\] in the above formula we get,
\[\omega = 2 \times \pi \times 50\]
\[\omega = 100\pi rad/\sec \]
This means that the speed of the turbine is \[100\pi \]\[rad/\sec \]. Which means that the turbine rotates \[100\pi \] radian in one second.
So the statement in the question represents the speed of the turbine or rotor.

Note:
To calculate the angular speed the angle we measure is in radians. The way of measuring angles is said to be radians. One full revolution will contain around \[6.28radians\]. Also, the angular speed and angular velocity make use of the same formula but the difference between the two is as we have seen before angular speed is a scalar quantity but angular velocity is a vector quantity.