Arc Length and Angular Velocity Word Problems

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Trigonometry Honors

1.1

Arc Length and Angular Velocity Word Problems

1. Find the angular velocity in radians per second of a wheel turning at 25 rpm.
2. The wheel of a truck is turning at 6 rps (revolutions per second). The wheel is 4 feet in diameter.
a. Find the angular velocity of the wheel in radians per second.
b. Find the velocity in feet per second of a point on the rim of the wheel.
3. Two pulleys, one 6 in. and the other 24 in. in diameter, are connected by a belt. The larger pulley revolves at a rate of 60 rpm.
a. Find the velocity of the belt in feet per minute.
b. Calculate the angular velocity of the smaller pulley in radians per minute.
4. Calculate the angular velocity in radians per minute of a Ferris wheel 250 feet in diameter that takes 45 seconds to rotate once. Express the answer in terms of p.
5. If you sat on the rim of the Ferris wheel in problem 4, what would your velocity be in feet per minute?
6. Calculate the angular velocity in radians per minute of a Ferris wheel 208 feet in diameter that takes 25 seconds to rotate once. Express the answer in terms of p.
7. If you sat on the rim of the Ferris wheel in problem 6, what would your velocity be in feet per minute?
8. Two pulleys are connected by a belt. The smaller pulley has a diameter of 8 cm and the larger pulley has a diameter of 12 cm. The smaller pulley is rotating at the rate of 60 rpm.
a. Find the angular velocity of each pulley in radians per second. Express the answer in terms of p.
b. Find the velocity of a point on the rim of each pulley in cm. per second.
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9. Two pulleys have a radii of 15 cm and 8 cm respectively. The larger pulley rotates 25 times in 36 seconds. Find the angular speed of each pulley in radians per second. Express your anwer in terms of p.



10. A 90-horsepower outboard motor at full throttle will rotate its propeller at 5000 rpm. Find the angular speed of the propeller in raidans per second.
11. The earth spins on its axis every 24 hours. If the earth’s circumference is 24,800 miles, find the velocity of a person standing on the equator in miles per hour.

Answers:

1.  5π/6 rad/sec

2a. 12π rad/sec

2b. 24π ft/sec

3a. 120π ft/min

3b. 480π rad/min

4. 8π/3 rad/min

5. 1000π/3 ft/min

6. 24π/5 rad/min

7. 2496π/5 ft/min

8a. small: 2π rad/sec & large: 4π/3 rad/sec

8b. small: 8π cm/sec & large: 8π cm/sec

9. small: 125π/48 rad/sec & large: 25π/18 rad/sec

10. 500π/3 rad/sec

11. 1033 1/3 mph

WASD |Trigonometry Honors / 2