This document contains formulas for arc length, area of a sector, linear speed, and angular speed. It provides examples of using these formulas to calculate the linear speed and angular speed of a Ferris wheel and test road speeds using a spin balancer on car wheels. Students are assigned problems from the textbook involving these concepts.

1. 5.1 Angles and Their Measure Formulas – Arc Length, Area of a Sector, Linear Speed, Angular Speed

2. Arc Length (s) s = arc length r = radius Θ = (theta) central angle (in radians)

3. Area of a Sector (A) A = area of the sector r = radius Θ = (theta) central angle (in radians)

4. Find the missing information

5. Find the missing information

6. Find the missing information

7. Find the missing information

8. Find the missing information

9. Find the missing information

10. Linear Speed (in circular motion) In distance unit per time unit

11. Angular Speed In radians per time unit

12. Consequence of these…

13. Ferris Wheel A neighborhood carnival has a Ferris wheel whose radius is 30 feet. You measure the time it takes for one revolution to be 70 seconds. What is the linear speed (in feet per second) of this Ferris wheel? What is the angular speed in radians per second?

14. Spin Balancing Tires A spin balancer rotates the wheel of a car at 480 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed is being tested? Express your answer in miles per hour.

15. Spin Balancing Tires For a diameter of 26 inches, at how many revolutions per minute should the balancer be set to test a road speed of 80 miles per hour?

16. Assignment p. 367 # 71 – 89 odd, 99 -103, 118, 119