PreCalculus
Angular and Linear Speed
Name: ___________________________
1. A circular saw blade has an angular speed of 15,000 radians per minute.
a. How many revolutions per minute does the saw make?
b. How long will it take the saw to make 6000 revolutions?
2. A circular gear rotates at the rate of 200 revolutions per minute (rpm).
a. What is the angular speed of the gear in radians per minute?
b. What is the linear speed of a point on the gear 2 inches from the center in inches per
minute? In feet per minute?
3. A wheel in large machine is 2.8 feet in diameter and rotates at 1200 rpm.
a. What is the angular speed of the wheel?
b. How fast is a point on the circumference of the wheel traveling in miles per hour?
4. A riding lawn mower has wheels that are 15 inches in diameter, which are turning at 2.5
revolutions per second.
a. What is the angular speed of a wheel?
b. How fast is the lawn mower traveling in miles per hour?
5. A bicycle has wheels that are 26 inches in diameter. If the bike is traveling at 14 mph, what is the
angular speed of each wheel?
6. A merry-go-round horse is traveling at 10 feet per second when the merry-go-round is making 6
revolutions per minute. How far is the horse from the center of the merry-go-round?
7. Find the length of the circular arc with the central angle whose radian measure is given. Assume
that the circle has diameter 10.
a. 1 radian
b. 2.2 radians
8. The second hand on a clock is 6 cm. How far does its tip travel in 40 seconds?
9. Find the area of the sector of a circle of radius 2 feet formed by an angle of 30. Round the
answer to two decimal places.
10. A water sprinkler sprays water over a distance of 30 feet while rotating through an angle of 135.
What area of the lawn receives water?