## Success in the portion of our class covering an Introduction to Rotation for a rigid system of particles is determined by your being able to accomplish the tasks listed below. The major objectives are listed by number. The list under each major objective includes both subtopics of that objective (usually topics which are required for a complete understanding of that major objective) and also the multiple representations of the task in which you are expected to be proficient. 1. Rotational Kinematics Apply the definitions of angular velocity and angular acceleration to rotational motion about a fixed axis Differential and integral forms of the definitions. Algebraic definitions of angular displacement, average angular velocity, average angular speed (spin rate), and average angular acceleration, all for rotational motion about a fixed axis Graphs of angular position, angular velocity, and angular acceleration versus time. Equations of angular position, angular velocity, and angular acceleration versus time. Quantitative calculations for: Any fixed-axis rotational motion with constant angular acceleration. Any fixed-axis rotational motion given either angular position, angular velocity, or angular acceleration versus time. 2. Rotational Dynamics - Force and Torque perspective Definition of rotational inertia for a given system of particles and a given axis Understand and apply the Parallel Axis Theorem Definition of torque for a selected force and a selected axis. Extended free-body diagrams Understand and apply Newton's Second Law for a system of particles (translation) Statics (sum of external forces equal zero and sum of torques equal zero about any and all axes) Understand and apply the rotational analog of Newton's Second Law for a rigid system of particles: For pure rotational motion about a fixed axis For translation of center of mass plus rotation about center of mass 3. Rotational Dynamics - Energy Perspective Work done by a torque over an angular displacement Instantaneous power of a torque applied to a rotating rigid system of particles Kinetic energy of a system of particles in pure rotation Kinetic energy of a system of particles with a translating center of mass and also rotating about the center of mass Conservation of Energy applied to systems of particles with rotational motion involved 4. Rolling without slipping, and also rotating and slipping As an example of applying Newton's Second Law for a system of particles, as well as the rotational analog of Newton's Second Law for a rigid system of particles As an example of applying the Conservation of Energy to a system of particles with rotational motion involved