Linear and Angular Speed Notes Answers

Pre-Calculus Arc Length, Linear/Angular Velocity Notes Name: Arc Length: Example 1: A circle has a radius of 4 inches. Find the length of the arc intercepted by a central angle of 240°. Example 2: Find 120° 4 in. s Example 3: Find the central angle (in radians and degrees) that is formed by a radius of 12 ft and an arc length of 1 ft Example 4: Find the distance between the cities. Assume that the Earth is a sphere of radius 0 miles and the cities are on the same longitude (one city is due north of the other). Johannesburg, South Africa Jerusalem, Israel 2 ° 1° Write a formula relating distance, rate and time: Linear Speed: Angular Speed: Equivalent ratios: Equivalent ratios: radians = °= revolution = circumference [ “units”] Example 5: The second hand of a clock is 10 2 cm long. Find the linear speed of the tip of the second hand in cm/s. Example 6: A 1 - inch diameter tire on a car makes a. Find the angular speed of the tire in rad/sec Example 7: b. Find the linear speed of the car in in/sec The circular blade on a saw has a diameter of revolutions per minute. a. Find the angular speed of the blade in rad/sec Example 8: revolutions per second. 2 inches and rotates at 4 00 b. Find the linear speed of the saw teeth (in ft/sec) as they contact the wood being cut. A woman is riding a bicycle whose wheels are 0 inches in diameter. If the wheels rotate at 1 0 rpm, find the speed at which she is traveling in mi/hr. Pre-Calculus Arc Length, Linear/Angular Velocity Homework Worksheet 1. Find the length of the arc in the figure. 2. Find the length of arc in the figure. 100° 140° 3. Find the length of an arc that subtends [forms] a central angle of 45° in a circle of radius 10 m. 4. Find the length of an arc that subtends [forms] a central angle of 2 rad in a circle of radius 2 mi. 5. An arc of length 100 m subtends [forms] a central angle measure of in radians and degrees. in a circle of radius 50 m. Find the 6. Find the radius of the circle if an arc of length 6 m on the circle subtends [forms] a central angle of rad. 7. Memphis, TN and New Orleans, LA lie approximately on the same meridian (longitude line). Memphis has a latitude 35°N and New Orleans has a latitude 30°N. Find the distance between these cities if the radius of the earth is 3960 mi. 8. A radial saw has a blade with a 6-in radius. Suppose the blade spins at 1000 rpm. a) Find the angular speed of the blade in rad/min. b) Find the linear speed of the saw teeth in ft/sec. 9. The wheels of a car have a diameter of 22 in and are rotating at 600 rpm. Find the speed of the car in mi/hr. 10. The earth rotates about its axis once every 23 h 56 min 4 s, and the radius of the earth is 3960 mi. Find the linear speed of a point on the equator in mi/hr. 11. A wind machine used to generate electricity has blades that are 10 ft in length. The propeller is rotating at 4 revolutions per second. Find the linear speed of the tips of the blades in ft/min. 12. The carousel at the county fair makes 3 revolutions per minute. a) Find the linear speed in ft/sec of a person riding a horse that is 22.5 ft from the center. b) The linear speed of the person on the inside of the carousel is 3.1 ft/sec. How far is this person from the center? c) How much faster is the rider on the outside going than the rider on the inside? Answers: 1. 12 22 units 6. m or 9. 2 mph 2. 1 20 units 11 4 m 7. 10. 10 mph 4 3. mi 11. 1 0 m 4. 4 mi 5. 8a. 2000 rad/min or 4 ft/min 12a. 2 2 rad or 1 rad/min 8b. 0 ft/sec 12b. ft 114 ° 2 12c. ft/sec ft/sec