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Transcript
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. t t Angular position, radians, measure counterclockwise. Angular velocity, radians per second. Angular acceleration, radians per second squared. Note that radians are a dimensionless quantity. Radians = Degrees * p/180 Example: 180 degrees = 3.14 radians Linear and Rotational Motion Compared x x v t v a t P mv F ma 1 2 K mv 2 Position Velocity Acceleration Momentum Force/Torque Kinetic Energy t t L I T I 1 2 K I 2 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: v2 ac r For constant angular speed, at = 0. Then, the acceleration is RADIAL, inwards. Figure 10-9 Rolling Without Slipping Figure 10-11 Velocities in Rolling Motion Figure 10-10 Rotational and Translational Motions of a Wheel Figure 10-12 Kinetic Energy of a Rotating Object K 1 2 mv 2 But… v r So… 1 2 K mv 2 1 2 mr 2 1 mr 2 2 2 Define the moment of inertia, I… I mr 2 K ROT 1 2 I 2 (it’s different for different shapes!) Moment of Inertia I mi ri i Vi 2 K Ki i Mi Ri Rigid body. Break up into small pieces Mi. What is the angular speed of each piece? 1 M iVi 2 i 2 1 M i Ri2i2 2 i 1 2 M i Ri2 2 i 1 2 I 2 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 A R The torque around point A is T = R x F Example: torque’s in balance 2r 2m 4f m