Chapter 9: Rotation of Rigid Bodies

Students learn to describe rotational motion through angular position, angular velocity, and angular acceleration, with angular velocity defined as a vector quantity following the right-hand rule and angular acceleration representing the time rate of change of angular velocity. The chapter presents kinematic equations for constant angular acceleration that directly parallel linear motion equations, enabling systematic analysis of rotating systems. A crucial connection emerges between rotational and translational motion, where points at distance r from the rotation axis experience tangential velocity proportional to both angular velocity and radial distance, while also experiencing centripetal acceleration directed toward the axis. The concept of moment of inertia appears as the rotational analog to mass, quantifying how mass distribution affects rotational resistance through discrete summation or continuous integration methods. The parallel-axis theorem provides a mathematical tool for calculating moment of inertia about any axis when the moment about the center of mass is known. Rotational kinetic energy, expressed as one-half the product of moment of inertia and angular velocity squared, extends energy conservation principles to rotating systems. The chapter demonstrates how work-energy methods apply to rotational motion, allowing students to solve complex dynamics problems involving both translational and rotational energy contributions to total mechanical energy.