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Trigonometry Name _________________________________________ Section 2.1 – Linear and Angular Speed Date ________________________ Pd _____________ 1. We will be describing speed of an object traveling on a circular path in two different ways. What are some units of measure for speed? 2. The Angular Speed (or Angular Velocity) of an object traveling on a circular path is the ratio of the angle through which the object travels to the time the object is traveling. In short: angle (in radians) angular speed time In symbols: t 3. The Linear Speed (or Linear Velocity) of an object traveling on a circular path is the ratio of the arc length through which the object travels to the time the object is traveling. In short: arc length linear speed time In symbols: v s r r t t 4. Angular Speed is measured in (radians/minute) or (revolutions/minute) 5. Linear Speed is measured in (centimeters/second) or (meters/minute) or (feet/sec) 6. Useful abbreviations: 7. Useful equivalences: 8. Hints for solving: s = arc length v = linear speed r = radius t = time seconds 1 minute = 60 1 hour = 60 minutes 1 day = 24 hours A = Area of a Sector = angular speed = angle (in radians) 1 mile = 5280 feet 1 revolution = 2 radians Read the question carefully to help determine which formula to use Use angular speed to calculate linear speed Pay attention to the required units of measure for the answer Use the equivalences (above, and others as needed) to help with conversions Examples: A. Consider the Earth, with a radius of approximately 4000 miles, which rotates on its axis once every 24 hours. What is the angular velocity of the Earth’s rotation in radians per hour? In degrees per hour? B. Consider a ceiling fan with radius of 2 feet that rotates 30 times per minutes. What is the angular velocity of the fan’s rotation in radians per hour? In degrees per hour? C. Back to the Earth … what is the linear velocity (in miles per hour) of the Earth’s rotation? D. What is the linear velocity (in miles per hour) of the ceiling fan? Note: Despite a much larger angular velocity, the tip of the blade of a ceiling fan has a much smaller linear velocity than the Earth because of the vast difference in the lengths of their respective radii. Homework: Page 453, #’s 95, 97. Use a calculator, and show all work!