3220 Classical Mechanics I covers vector operations, coordinate transformations, derivatives of vectors, Newton’s laws of motion, differential equations, alternative coordinate systems, kinematics and dynamics of a particle, air resistance, momentum of a time varying mass, center of mass systems, angular momentum, moment of inertia, energy, work-energy theorem, forces as the gradient of potential energy, time dependent potential energy, curvilinear one-dimensional systems, energy of a multi-particle system, calculus of variations, Lagrangian dynamics.

CO: PHYS 2820 and Mathematics 2260, 3202
PR: PHYS 2820 and Mathematics 2260

PHYS 3220 builds on the topics covered in PHYS 1050/1051 and PHYS 2820 by introducing concepts that allow real-life problems to be solved. The motion of a projectile is revisited taking the effects of air resistance into consideration. From this, students learn how to include additional forces necessary to model the motion of objects under a variety of conditions. The concept of momentum is extended to include the motion of objects with variable mass, such as rockets, giving students the knowledge to solve complex problems such as a the force required to lift a chain upwards from a rest position. Students taking this course will also expand their understanding of the relationship between work and energy and apply the concept of line integrals to calculate the work done along a described path. In the last part of this course, students will learn to solve advanced problems in mechanics using Lagrangian dynamics. The Lagragian formalism, based on the kinetic energy and potential energy of the system, allows for scenarios too complicated to be treated using Newtonian dynamics to be analyzed and solved with relative ease. This course is a prerequisite for the follow-up course PHYS 3230 Classical Mechanics II.