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**3.3 Angular & Linear Velocity**

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Yesterday arc length We can use it to analyze motion of a circular path (like tires, gears, & Ferris Wheels) A point on the edge of a wheel will move through an angle called angular displacement (in radians) To find angular displacement, multiply the rotations times 2π (1 time around in radians) Ex 1) A gear makes 1.5 rotations about its axis. What is angular displacement in radians of a point on the gear? (1.5)(2π) = 3π ≈ 9.4 rad

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**We can calculate angular velocity**

*We will have to be very aware of the units of our answer. Most often we will have to convert to the correct units. Always include the unit labels & it will be easy to see what you need to get & cancel!! (called dimensional analysis) angular displacement (radians) unit of time

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Ex 2) Find the angular velocity in radians per second of a point on a gear turning at the rate of 3.4 rpm (rpm = revolutions per minute) Ex 3) What is the angular velocity in radians per second of a notch on a wheel turning at a rate of 7600 rpm?

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**To calculate linear velocity v**

If you have a circle with 2 points on it at different distances from the center A & B will have the same angular velocity but different linear velocities. B A O B will travel further! To calculate linear velocity v

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Ex 4) An ice skater moves around the edge of a circular rink at a rate of 2 rpm. The rink has a radius of 4.1 m. What is the skater’s velocity in meters per minute?

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**Ex 5) A unicycle has a tire with radius 10 in**

Ex 5) A unicycle has a tire with radius 10 in. It is traveling at a speed of 5.5 mph a) Find the angular velocity of the tire in radians per second (miles per hour) Since b) How many revolutions per second does the tire make?

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Ex 6) Determine the linear velocity (in cm per second) of a point on the circle 5 cm from the center that moves through an angle of 56° in 1 min

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Homework #303 Pg #1–23 odd, 25, 27, 31, 34, 35, 41, 42, 43

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Angles and Radian Measure Section 4.1. Objectives Estimate the radian measure of an angle shown in a picture. Find a point on the unit circle given one.

Angles and Radian Measure Section 4.1. Objectives Estimate the radian measure of an angle shown in a picture. Find a point on the unit circle given one.

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