College Physics

Introduction to Rotational Motion and Angular Momentum

College PhysicsIntroduction to Rotational Motion and Angular Momentum

Chapter Outline

10.1 Angular Acceleration
• Describe uniform circular motion.
• Explain non-uniform circular motion.
• Calculate angular acceleration of an object.
• Observe the link between linear and angular acceleration.
10.2 Kinematics of Rotational Motion
• Observe the kinematics of rotational motion.
• Derive rotational kinematic equations.
• Evaluate problem solving strategies for rotational kinematics.
10.3 Dynamics of Rotational Motion: Rotational Inertia
• Understand the relationship between force, mass and acceleration.
• Study the turning effect of force.
• Study the analogy between force and torque, mass and moment of inertia, and linear acceleration and angular acceleration.
10.4 Rotational Kinetic Energy: Work and Energy Revisited
• Derive the equation for rotational work.
• Calculate rotational kinetic energy.
• Demonstrate the Law of Conservation of Energy.
10.5 Angular Momentum and Its Conservation
• Understand the analogy between angular momentum and linear momentum.
• Observe the relationship between torque and angular momentum.
• Apply the law of conservation of angular momentum.
10.6 Collisions of Extended Bodies in Two Dimensions
• Observe collisions of extended bodies in two dimensions.
• Examine collision at the point of percussion.
10.7 Gyroscopic Effects: Vector Aspects of Angular Momentum
• Describe the right-hand rule to find the direction of angular velocity, momentum, and torque.
• Explain the gyroscopic effect.
• Study how Earth acts like a gigantic gyroscope.
Figure 10.1 The mention of a tornado conjures up images of raw destructive power. Tornadoes blow houses away as if they were made of paper and have been known to pierce tree trunks with pieces of straw. They descend from clouds in funnel-like shapes that spin violently, particularly at the bottom where they are most narrow, producing winds as high as 500 km/h. (credit: Daphne Zaras, U.S. National Oceanic and Atmospheric Administration)

Why do tornadoes spin at all? And why do tornados spin so rapidly? The answer is that air masses that produce tornadoes are themselves rotating, and when the radii of the air masses decrease, their rate of rotation increases. An ice skater increases her spin in an exactly analogous manner as seen in Figure 10.2. The skater starts her rotation with outstretched limbs and increases her spin by pulling them in toward her body. The same physics describes the exhilarating spin of a skater and the wrenching force of a tornado.

Clearly, force, energy, and power are associated with rotational motion. These and other aspects of rotational motion are covered in this chapter. We shall see that all important aspects of rotational motion either have already been defined for linear motion or have exact analogs in linear motion. First, we look at angular acceleration—the rotational analog of linear acceleration.

Figure 10.2 This figure skater increases her rate of spin by pulling her arms and her extended leg closer to her axis of rotation. (credit: Luu, Wikimedia Commons)