090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
Wednesday, September 7, 2016
Trigonometry Period 2
Lesson Overview:
• Warm Up
• Go over homework
• Unit 1: Radian Measure
> Linear and Angular Velocity
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
Warm Up:
Sketch the following angles in standard position. Then provide two coterminal angles for each (one positive, one negative). Express your answer in the units given in the problem.
Coterminal (+): ___________
Coterminal (­): __________ Coterminal (+): ___________
Coterminal (­): __________ 2
090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
3. Find the arc length given θ = 90° and radius measuring 10m
4. Find the measure of θ given arc length measuring 42 inches and radius measuring 3 inches.
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090716 Linear Angular Speed Day3 Pd2.notebook
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
Questions on the homework?
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090716 Linear Angular Speed Day3 Pd2.notebook
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090716 Linear Angular Speed Day3 Pd2.notebook
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090716 Linear Angular Speed Day3 Pd2.notebook
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LINEAR and ANGULAR Velocity (Speed)
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
5. A racecar is driving at 170 mph. The diameter of the tires is 18
inches.
A. Find the number of revolutions per minute of the cars tires.
B. Find the number of revolutions per second of the cars tires.
C. Find the angular speed of the car in degrees per second.
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
6. Michelle Kwan‛s performance contains a camel spin. The length of
her leg is 31 inches. She spins at a rate of 1.5 revolutions per
second.
A. Find the speed of the tip of her toe in feet per second
B. Find the speed of the tip of her toe in miles per hour.
C. Find her angular speed in degrees per second.
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
1. Find the angular speed (in radians per second) for each of the following:
a. The hour hand of a clock
b. The minute hand of a clock
c. The line from the center to the edge of a CD revolving 300 times per minute
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
2. Suppose that a point P is on circle O with radius r = 20 cm and ray OP has an angular speed of radians per second. Find
a. The angle generated by P in 6 seconds
b. The distance traveled by P along the circle in 6 seconds
c. The linear speed of P
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
3. Suppose that a machine contains a wheel of diameter 3feet, rotating at a rate of 1600 rp
a. Find the angular speed of the wheel.
b. Find the linear speed of a point on the circumference of the wheel.
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
4. A typical tire for a compact car is 22 inches in diameter. If the car is traveling at a speed of 60mph, find the number of revolutions the tire makes per minute.
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
5. The Earth revolves on its axis once every 24 hours. Assuming that Earth’s radius is 6400 km, find the following:
a. Angular speed of Earth in radians per day, then radians per hour.
b. Linear speed at the North or South Pole.
c. Linear speed at Quito, Ecuador, a city on the equator.
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
6. A Ferris wheel rotates 3 times each minute. The passengers sit in seats that are 25 feet from the center of the wheel.
a. What is the angular velocity of the wheel in degrees per minute and radians per minute?
b. What is the linear velocity of the passengers in the seats?
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090716 Linear Angular Speed Day3 Pd2.notebook
September 07, 2016
Homework:
1. HW6 Worksheet on Unit 1 Review Topics
2. Celebration of Knowledge on Unit 1 scheduled for Friday,
September 9th
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