Name:____________________________Date:____________________________
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 .
5. If you sat on the rim of the Ferris wheel in problem 4, what would your velocity be in
feet per minute?
WASD |Trigonometry Honors 1
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 .
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 .
b. Find the velocity of a point on the rim of each pulley in cm. per second.
.
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 .
WASD |Trigonometry Honors 2
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 3