Question 4.1.9: Finding Linear Speed A wind machine used to generate electri...
Finding Linear Speed
A wind machine used to generate electricity has blades that are 10 feet in length (see Figure 4.18). The propeller is rotating at four revolutions per second. Find the linear speed, in feet per second, of the tips of the blades.
We are given ω, the angular speed.
ω = 4 revolutions per second
We use the formula v=r \omega to find y, the linear speed. Before applying the formula, we must express ω in radians per second.
\omega=\frac{4 \cancel{ revelutions }}{1 \text { second }} \cdot \frac{2 \pi \text { radians }}{1 \cancel{ revelution }}=\frac{8 \pi \text { radians }}{1 \text { second }} \text { or } \frac{8 \pi}{1 \text { second }}
The angular speed of the propeller is 8π radians per second. The linear speed is
v=r \omega=10 \text { feet } \cdot \frac{8 \pi}{1 \text { second }}=\frac{80 \pi \text { feet }}{\text { second }}.
The linear speed of the tips of the blades is 80π feet per second, which is approximately 251 feet per second.