Introductory Classical Mechanics

PHYS3904 Theoretical Methods in Medical Physics

Two hours One requisite

1 Fundamental Concepts Vectors / Revision of vectors / Triple products / Derivative of a vector / Position vector of a particle velocity and acceleration in rectangular coordinates. / Velocity and acceleration in polar coordinates. / Velocity and acceleration in cylindrical and spherical coordinates

2 Newtonian Mechanics, Rectilinear Motion of a Particle / Newton's law of motion. / Rectilinear Motion: uniform Acceleration under a constant force. / Position-dependent forces. / The Concepts of kinetic and potential energy. / Velocity-dependent forces. / Fluid resistance and terminal velocity. / Linear Resorting Force: harmonic motion. / Energy considerations in harmonic motion. / Damped harmonic motion. / Forced harmonic motion: resonance

3 General Motion of a Particle in Three Dimensions / The potential energy function in three-dimensional motion / The del operator / Forces of the separable type. / The harmonic oscillator in two and three dimensions. / Constrained motion of a particle. / Motion of Charged Particles in Electric and Magnetic Fields / Simple pendulum. / More accurate solution of the simple pendulum problem

4 Noninertial Reference Systems / Accelerated coordinate systems and inertial forces. / Rotating coordinate systems. / Dynamics of a particle in a rotating coordinate system. / Effects of earth's rotation. / The Foucault pendulum

5 Gravitation and Central Forces / • Introduction. / • Gravitational force between a uniform sphere and a particle. / • Kepler's laws of planetary motion. / • Kepler's second law: equal areas. / • Kepler's first law: The law of ellipses. / • Kepler's third law: The harmonic law. / • Potential energy in a gravitational field: gravitational potential. / • Potential energy in a general central field. / • Energy equation of an orbit in a central field

6 Dynamics of Systems of Particles / • Center of mass and linear momentum of a system. / • Angular momentum and kinetic energy of a system. / • Motion of two interacting bodies: the reduced mass. / • Collisions. / • Oblique collisions and scattering: comparison of laboratory and / center of mass coordinates. / • Motion of a body with variable mass: rocket motion

1.1 Mapped to: K1

Define the physical quantities related to the motion of a single particle.

Teaching Strategy Lectures