1. 1 The line from the center sweeps out a central angle  in an amount time t, then the angular velocity, (omega) Angular Speed: the amount of rotation per unit of time, where  is the angle of rotation and t is the time. 3.5 Angular and Linear Speed

2. 2 Formulas for Angular ( in radians per unit time,  in radians) Linear SpeedAngular Speed

3. 3 Example: Using the Formulas Suppose that point P is on a circle with radius 20 cm, and ray OP is rotating with angular speed radian per second. a) Find the angle generated by P in 6 sec. b) Find the distance traveled by P along the circle in 6 sec. c) Find the linear speed of P.

4. 4 Solution: Find the angle. The speed of ray OP is radian per second.

5. 5 Solution: Find the angle continued The distance traveled by P along the circle is

6. 6 Solution: Find the angle continued linear speed

7. 7 Example: A belt runs a pulley of radius 6 cm at 80 revolutions per min. a) Find the angular speed of the pulley in radians per second. 80(2  ) = 160  radians per minute. 60 sec = 1 min b) Find the linear speed of the belt in centimeters per second. The linear speed of the belt will be the same as that of a point on the circumference of the pulley.