a windmill for generating electricity has a blade that is 30 feet long. find the angular velocity in rad/sec…

a windmill for generating electricity has a blade that is 30 feet long. find the angular velocity in rad/sec for the tip of the blade if the windmill is rotating at a rate of 436.1 rev/min. the angular velocity is rad/sec. (type an integer or decimal rounded to the nearest tenth as needed.)

a windmill for generating electricity has a blade that is 30 feet long. find the angular velocity in rad/sec for the tip of the blade if the windmill is rotating at a rate of 436.1 rev/min. the angular velocity is rad/sec. (type an integer or decimal rounded to the nearest tenth as needed.)

Answer

Explanation:

Step1: Convert revolutions per minute to revolutions per second

Since (1) minute ( = 60) seconds, we divide the number of revolutions per minute by (60). (436.1\div60=\frac{436.1}{60}\text{ rev/sec})

Step2: Use the conversion factor for radians

One revolution is (2\pi) radians. So, to find the angular velocity (\omega) in radians per second, we multiply the number of revolutions per second by (2\pi). (\omega=\frac{436.1}{60}\times2\pi) [ \begin{align*} \omega&=\frac{436.1\times2\pi}{60}\ &=\frac{872.2\pi}{60}\ &\approx\frac{872.2\times3.14159}{60}\ &=\frac{2740.27}{60}\ &\approx45.7 \end{align*} ]

Answer:

(45.7)