11. A wind turbine has three blades, each measuring 3 m from centre to tip. At a particular time, the turbine is rotating four times a minute.
a) Determine the angular velocity of the turbine in radians/second.

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Explanation:

The blade completes 4 full rotations every 1 minute. This is the same as saying it does 4 full rotations every 60 seconds.

Let's divide both parts of that by 4 to get

So "4 full rotations every 60 seconds" becomes "1 full rotation every 15 seconds".

We can then set up the following expression:

Notice that the "rotation" units cancel out when dividing. The first fraction represents having 1 rotation per 15 seconds. The second fraction is based on the fact that 1 full rotation is 2pi radians.

Simplifying that said expression leads to this:

This indicates that for every second, the blade is rotating 2pi/15 radians.

Side note: the radius of 3 meters is never used. It would only be useful if we wanted to know the linear velocity of the blade tip.

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