2 Yesterday arc lengthWe 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
3 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
4 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?
5 To calculate linear velocity v If you have a circle with 2 points on it at different distances from the centerA & B will have the same angular velocity but different linear velocities.BAOB will travel further!To calculate linear velocity v
6 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?
7 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 mpha) Find the angular velocity of the tire in radians per second(miles per hour)Sinceb) How many revolutions per second does the tire make?
8 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