1. Chapter 8 Rotational Kinematics

2. Radians

3. Angular Displacement  Angle through which something is rotated  Counterclockwise => positive(+) Units => radians

4. Angular Speed  Rate of Rotation  Counterclockwise => positive(+)  Clockwise => negative(-)  Units => radians/second  Also rev/min or rpm

5. Angular Acceleration  Units => radians/second 2  Rate of change of angular speed  Counterclockwise => positive(+)  Clockwise => negative(-)

6. Linear vs. Angular Quantities  Linear xx vv aa  Angular    (m) (m/s) (m/s 2 ) (rad) (rad/s) (rad/s 2 )

7. Linear vs. Angular Quantities  Linear  Angular

8. Warm-up  A ceiling fan’s angular speed increases from 5.2 rad/s to 20.9 rad/s. During this constant angular acceleration, the fan moves through an angular displacement of 216 rad. How long does it take the fan to reach its final angular speed?

9. Tangential Velocity  Instantaneous linear speed of an object tangent to a circular path  Objects with the same angular speed, may have different tangential speeds  m/s

10. Tangential Acceleration  Instantaneous linear acceleration of an object tangent to a circular path  Objects with the same angular acceleration, may have different tangential accelerations  m/s 2

11. Centripetal Acceleration  Always directed towards the center of the circle

12. Total Acceleration  Tangential and centripetal acceleration are perpendicular to one another Use Pythagorean’s theorem to find the total acceleration. Angle ϕ is measured relative to the radius.

13. Rolling Motion  Assuming that a wheel rolls without slipping, then  The Tangential speed of a point on the outside of the wheel will equal the linear velocity.  The tangential acceleration of a point on the outside of the wheel will equal the linear acceleration.