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286 Chapter 4 Trigonometry<br />
Example 6<br />
Finding Linear Speed<br />
FIGURE 4.16<br />
10.2 cm<br />
The second hand of a clock is 10.2 centimeters long, as shown in Figure 4.16. Find the<br />
linear speed of the tip of <strong>this</strong> second hand as it passes around the clock face.<br />
Solution<br />
In one revolution, the arc length traveled is<br />
s 2r<br />
210.2<br />
20.4 centimeters.<br />
Substitute for r.<br />
The time required for the second hand to travel <strong>this</strong> distance is<br />
t 1 minute 60 seconds.<br />
So, the linear speed of the tip of the second hand is<br />
116 ft<br />
Linear speed s t<br />
20.4 centimeters<br />
60 seconds<br />
1.068 centimeters per second.<br />
Now try Exercise 111.<br />
Example 7<br />
Finding Angular and Linear Speeds<br />
The blades of a wind turbine are 116 feet long (see Figure 4.17). The propeller rotates<br />
at 15 revolutions per minute.<br />
a. Find the angular speed of the propeller in radians per minute.<br />
b. Find the linear speed of the tips of the blades.<br />
FIGURE 4.17<br />
Solution<br />
a. Because each revolution generates radians, it follows that the propeller turns<br />
152 30 radians per minute. In other words, the angular speed is<br />
Angular speed <br />
t<br />
b. The linear speed is<br />
<br />
30 radians<br />
1 minute<br />
2<br />
30 radians per minute.<br />
Linear speed s t<br />
r<br />
t<br />
11630 feet<br />
1 minute<br />
Now try Exercise 113.<br />
10,933 feet per minute.
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