Answer: 2pi/15 radians per 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:
[tex]\frac{1 \text{ rotation}}{15\text{ seconds}}*\frac{2\pi \text{ radians}}{1 \text{ rotation}}\\\\[/tex]
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:
[tex]\frac{1 \text{ rotation}}{15\text{ seconds}}*\frac{2\pi \text{ radians}}{1 \text{ rotation}} = \frac{1*2\pi}{15*1} \frac{\text{radians}}{\text{second}}= \frac{2\pi}{15} \text{ radians per second}[/tex]
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.
