2Yesterday 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
3We 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
4Ex 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?
5To 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
6Ex 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?
7Ex 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?
8Ex 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