Angular Motion Chapter 10

Figure 10-1 Angular Position

Figure 10-2 Arc Length

Figure 10-3 Angular Displacement

Figure 10-4 Angular Speed and Velocity

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.

Figure 10-5 Angular Acceleration

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

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

Figure 10-7 Angular and Linear Speed

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

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.

Figure 10-9 Rolling Without Slipping

Figure Velocities in Rolling Motion

Figure Rotational and Translational Motions of a Wheel

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

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

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

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