PHYS 306

INTERMEDIATE MECHANICS

Catalog Entry

PHYS 306. Intermediate Mechanics

Three hours lecture (3).

Prerequisites: PHYS 222 and MATH 152.

Study of theoretical and applied Newtonian mechanics including position and velocity dependent forces, oscillations, stability, non-inertial frames and gravitation from extended bodies.

Detailed Description of Content of Course

This class will concentrate on classical Newtonian mechanics and its applications to a number of real-world systems. Topics to be studied in this class include:

- Newton's Laws of Motion
- Classical Mechanics
- Newton's First and Second Laws; Inertial Frames
- The Third Law and Conservation of the Momentum
- Newton's Second Law in Cartesian Coordinates
- Two-Dimensional Polar Coordinates
- Position and velocity dependent forces

- Projectiles and Charged Particles
- Air Resistance
- Trajectory and Range in a Linear Motion
- Motion of a Charge in a Uniform Magnetic Field
- Complex Exponentials
- Solution for the Charge in a B Field

- Momentum and Angular Momentum
- Conservation of Momentum
- Rockets
- The Center of Mass
- Angular Momentum

- Energy
- Kinetic Energy and Work
- Potential Energy and Conservative Forces
- Force as the Gradient of Potential Energy
- Time-Dependent Potential Energy
- Central Forces and Gravity
- Energy of Interaction of Two Particles
- The Energy of a Multiparticle System

- Oscillations
- Hooke's Law
- Simple Harmonic Motion
- Two-Dimensional Oscillators
- Damped Oscillators
- Driven Damped Oscillations
- Resonance
- Fourier Series

- Calculus of Variations
- The Euler-Lagrange Equation
- Applications of the Euler-Lagrange Equation

- Lagrange's Equations
- Lagrange's Equations for Unconstrained Motion
- Constrained Systems
- Conservation Laws in Lagrangian Mechanics
- Lagrange's Equations for Magnetic Forces
- Lagrange Multipliers and Constraint Forces

- Two-Body Central Force Problems and Gravity
- Newton’s Law of Gravitation
- Center of Mass and Relative Coordinates
- Reduced Mass
- Keplerian Orbits

- Mechanics in Noninertial Frames
- Acceleration without Rotation
- Tides
- Angular Velocity
- Newton's Second Law in a Rotating Frame
- Coriolis Force and Coriolis Acceleration

- Motion of Rigid Bodies
- Rotation about a Fixed Axis
- Rotation about Any Axis
- Inertia Tensor and Principal Axes of Inertia
- Principal Axes and Eigenvalue Equations
- Euler's Equations

- Coupled Oscillators and Normal Modes
- Coupled Pendulums
- Lagrangian methods
- Normal Coordinates

Detailed Description of Conduct of Course

The class format will be lecture/discussion. Part of the class time will be used for the development of the formal theory while the rest of the meeting time will be devoted to solving example problems. The majority of students’ time outside of the classroom will be spent in working on problems. Some of the assigned problems may be computer-based.

Goals and Objectives of the Course

The following student abilities are expected to be developed or enhanced due to this course:

- Students will be able to apply Newton’s Laws to a broad range of physical systems.
- Students will be able to solve problems involving both static and dynamic systems.
- Students will develop proficiency in the basic mathematical methods used in everyday physics.

Assessment Measures

Student comprehension of the material will be based on instructor feedback on assigned homework problems, in-class discussions and students’ presentation of their solutions, and periodic exams.

Other Course Information

None

APPROVAL AND SUBSEQUENT REVIEW

DATE ACTION REVIEWED BY

New Course February 2, 2006