College Physics, 7th Edition Lecture Outline Chapter 8 College Physics, 7th Edition Wilson / Buffa / Lou © 2010 Pearson Education, Inc.

Units of Chapter 8 Rotational Motion and Equilibrium Rigid Bodies, Translations, and Rotations Torque, Equilibrium, and Stability Rotational Dynamics [Not tested on AP Physics B] Rotational Work and Kinetic Energy [Not tested on AP Physics B] Angular Momentum [Not tested on AP Physics B] © 2010 Pearson Education, Inc.

FOCUSED LEARNING TARGET GIVEN AN OBJECT WITH A TENDENCY TO ROTATE CLOCKWISE AND COUNTER CLOCKWISE ( WITH A RIGID OR FIXED FULCRUM ) AND ROLL , I WILL BE ABLE TO CALCULATE THE TORQUE USING Ƭ= rF , ANGULAR VELOCITY AND TRANSLATIONAL VELOCITY USING VCM = rω AND ACHIEVE MECHANICAL EQUILIBRIUM USING THESE CONDITIONS: ƩƬ =0 AND ƩF =0

8.1 Rigid Bodies, Translations, and Rotations A rigid body is an object or a system of particles in which the distances between particles are fixed (remain constant). Rigid bodies only exist in a perfect, IDEAL world! In other words, a rigid body must be solid (but not all solid bodies are rigid). A quantity of liquid water is not a rigid body, but when water freezes into ice it becomes a rigid body. In reality, the particles of a solid vibrate constantly, and undergo elastic and inelastic collisions. © 2010 Pearson Education, Inc.

8.1 Rigid Bodies, Translations, and Rotations A rigid body may have either two types of motion or both: 1. Translational 2. Rotational What’s the difference between the two? You can combine both types of forces and that’s where we get the term ROLLING! © 2010 Pearson Education, Inc.

8.1 Rigid Bodies, Translations, and Rotations For an object that is rolling without slipping, s = rθ a = rα An object can roll with slipping, but none of the equations will hold when there is slipping. © 2010 Pearson Education, Inc.

CW :P 295 #8,9,12,11a

8.1 Rigid Bodies, Translations, and Rotations A cylinder rolls on a horizontal surface without slipping. The cylinder has a radius of 12 cm and a center of mass speed of 0.10 m/s as it rolls without slipping. If it continues to travel at this speed for 2.0s, through what angle does the cylinder rotate during this time?

8.2 Torque, Equilibrium, and Stability The perpendicular distance from the line of force to the axis of rotation is called the lever arm or the moment arm. [symbol r, (like radius) The product of the force and the lever arm is called the torque. It takes a force to start an object rotating; that force is more effective the farther it is from the axis of rotation, and the closer it is to being perpendicular to the line to that axis. S.I. Unit: m N © 2010 Pearson Education, Inc.

8.2 Torque, Equilibrium, and Stability Torque in rotational motion can be thought of as the analogue of force in translational motion. Torque (rotational) is similar to Force (linear) © 2010 Pearson Education, Inc.

8.2 Torque, Equilibrium, and Stability Torque is a vector or scalar???? Counterclockwise is positive, and clockwise is negative. © 2010 Pearson Education, Inc.

CW: p 295- 296 22,23

8.2 Torque, Equilibrium, and Stability In the human body torques produced by the contraction of muscles cause some bones to rotate at joints. With the axis of rotation through the elbow joint and the muscle attached 4.0 cm from the joint, what are the magnitudes of the muscle torques for cases a and b if the muscle exerts a force of 600 N.

8.2 Torque, Equilibrium, and Stability In order for an object to be in equilibrium, the net force on it must be zero, and the net torque on it must be zero as well. Equilibrium means that forces and torques are in balance. Can be at ______ or at _________ __________. © 2010 Pearson Education, Inc.

8.2 Torque, Equilibrium, and Stability Two types of equilibrium: Translational linear; forces Rotational circular; torques Mechanical Equilibrium Static Equilibrium

8.2 Torque, Equilibrium, and Stability Concurrent Forces vs. Couple © 2010 Pearson Education, Inc.

8.2 Torque, Equilibrium, and Stability A picture hangs motionless on a wall. If the picture has a mass of 3.0 kg, what are the magnitudes of the tension forces in the wires?

8.2 Torque, Equilibrium, and Stability Three masses are suspended from a meter stick. How much mass must be suspended on the right side for the system to be in static equilibrium? [Neglect the mass of the meter stick] © 2010 Pearson Education, Inc.

8.2 Torque, Equilibrium, and Stability If an object is in stable equilibrium, any displacement from the equilibrium position will create a torque that tends to restore the object to equilibrium. Otherwise the equilibrium is unstable. © 2010 Pearson Education, Inc.

8.2 Torque, Equilibrium, and Stability Whether equilibrium is stable or unstable depends on the width of the base of support. © 2010 Pearson Education, Inc.