1. Angular Motion Chapter 10

2. Figure 10-1 Angular Position

3. Figure 10-2 Arc Length

4. Figure 10-3 Angular Displacement

5. Figure 10-4 Angular Speed and Velocity

6. Angular Speed is a Vector! We use a “right hand rule” to determine the vector direction of a rotation. Using your right hand, curl your fingers in the direction of the rotation. Your thumb points in the direction of the rotation. Works for angular acceleration as well.

7. Figure 10-5 Angular Acceleration

8. Summary of angular motions. Angular position, radians, measure counter- clockwise. Angular velocity, radians per second. Angular acceleration, radians per second squared. Note that radians are a dimensionless quantity. Radians = Degrees *  /180 Example: 180 degrees = 3.14 radians

9. Linear and Rotational Motion Compared Position Velocity Acceleration Momentum Force/Torque Kinetic Energy

10. Figure 10-7 Angular and Linear Speed

11. Conceptual Checkpoint 10-1 How do the angular speeds compare? V=r  How do the linear speeds compare?

12. Figure 10-8 Centripetal and Tangential Acceleration IMPORTANT: For uniform circular motion, The centripetal acceleration is: For constant angular speed, a t = 0. Then, the acceleration is RADIAL, inwards.

13. Figure 10-9 Rolling Without Slipping

14. Figure 10-11 Velocities in Rolling Motion

15. Figure 10-10 Rotational and Translational Motions of a Wheel

16. Figure 10-12 Kinetic Energy of a Rotating Object But… So… Define the moment of inertia, I… (it’s different for different shapes!)

17. Moment of Inertia ViVi MiMi RiRi Rigid body. Break up into small pieces M i. What is the angular speed of each piece?

18. Rotational force: Torque Torque is the “twisting force” that causes rotational motion. It is equal to the magnitude of the component of an applied force perpendicular to the arm transmitting the force. F R A The torque around point A is T = R x F

19. Example: torque’s in balance 2r4f 2m m