MINISTRY OF EDUCATION ST. MARY’S SCHOOL MATH AND PHYSICS DEPARTMENT Grade: ___________ III QUARTER TRIGONOMETRY 10TH – CLASSWORK # 1 – LINEAR AND ANGULAR SPEED Name: Date: 04/05/2021 Group: 10 Score: _______/80 Teacher: Arlhem Wynter S. Due Date: 04/05/2021 at 8:25 AM Total: 80 points INSTRUCTIONS: Show the entire procedure to support your answers. The use of a calculator is permitted. Do not scratch. Do not use liquid corrector. Use pencil for procedures, ink for final answers. Be organized. I. Problem Solving. Solve the problems. Show the entire procedures (data, diagrams, equations, and answers). Significant figures are taken into consideration. 10 points each. 1. Ferris Wheel Problem. Dan Druff and Ella Funt decide to ride on a Ferris Wheel in a neighborhood carnival. Dan measures the time, and he observes that it takes 70 seconds to make a complete revolution. Their seats are 30 feet away from the axle of the wheel. Find the following: a) What is the linear speed (in miles per hour) of this Ferris wheel? b) What is their angular speed in radians per minute? In degrees per minute? 2. Car Tire Problem. 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. At how many revolutions per minute should the balancer be set to test a road speed of 80 miles per hour? 3. Clock Problem. The minute hand on Mr. Incredible’s watch is 0.25 inches long. Find the angular velocity and linear velocity of the end of the minute hand in each of the following: a) How fast is the tip of the minute hand moving? Give your answer in feet per minute. b) Find the angular velocity of the minute hand on the clock in radians per hour. 4. Train Problem. (5 points). A train wheel has a diameter of 30 inches to the rim, which rests on the track. The flange, which keeps the wheel from slipping off the track, projects 1 inch beyond the rim. When the train is traveling 60 mph, what is the linear velocity of a point on the outer edge of the flange? 5a. Gear Problem. A large gear of diameter 30 cm is revolving at 45 rpm. It drives the small gear of diameter 8 cm. (5 points). Find: a) At how many radians per hour is the large gear turning? b) What is the linear velocity of the teeth on the large and small gear? c) At how many revolutions per second is the small gear turning? 5.b Pulley Problem. A small pulley 6 cm in diameter is connected by a belt to a larger pulley 15 cm in diameter. The small pulley is turning with an angular velocity of 120 radians per minute. (5 points). Find: a) The linear velocity of the rim of the small pulley and the large pulley. b) Find the angular velocity of the large pulley in rot/sec. c) What is the angular velocity of a point at the center of the large pulley? 6. Earth Problem. The earth rotates about its axis once every 23 hours, 56 minutes, and 4 seconds with the radius of the Earth being 3960 miles. It also revolves around the sun in an orbit that is approximately circular with a radius of 9.3107 mi. (15 points) Find : a) The linear speed of a point on the equator in miles per hour. b) The radius of orbit sweeps out an angle with what exact angular velocity (in radians per hour, to two decimal places)? c) How fast (to the nearest hundred miles per hour) is the earth traveling around its orbit? 7. Business Company Problem. (5 points) A Ford Expedition comes standard with tires that have a diameter of 25 inches. If the owner decided to upgrade to tires with a diameter of 30 inches without having the onboard computer updated, how fast will the Expedition actually be traveling when the speedometer reads 75 mph? 8a. Lawn Mower Blade Problem. In order for a lawn mowver blade to cut grass, it must strike the grass with a speed of at least 900 inches per second. (10 points) a) If the innermost part of the cutting edge is 6 inches from the center of the blade, how many radians per second must the blade turn? How many revolutions per minute is this? b) The blade has a diameter of 19 inches. If the outermost tip of the blade hits a rock while turning as in part (a), how fast could the rock be hurled from the mower. 8b. Lawn Mower Cord Problem. Yank Hardy pulls a cord on his power mower. In order for the engine to start, the pulley must turn at 64, 800 degrees per minute. The pulley has a radius of 0.2 feet. (5 points) a) At how many radians per second must the pulley turn in 13 seconds? b) How fast must Yank pull the cord to start the mower? c) When Yank pulls this hard, what is the angular velocity of the center of the pulley?
