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Classical Mechanics PHYS 2006 Tim Freegarde Classical Mechanics LINEAR MOTION OF SYSTEMS OF PARTICLES centre of mass Newton’s 2nd law for bodies (internal forces cancel) rocket motion rotations and infinitessimal rotations ANGULAR MOTION angular velocity vector, angular momentum, torque parallel and perpendicular axis theorems rigid body rotation, moment of inertia, precession conservative forces, law of universal gravitation GRAVITATION & KEPLER’S LAWS 2-body problem, reduced mass planetary orbits, Kepler’s laws energy, effective potential NON-INERTIAL REFERENCE FRAMES NORMAL MODES centrifugal and Coriolis terms Foucault’s pendulum, weather patterns coupled oscillators, normal modes boundary conditions, Eigenfrequencies 2 Rotating coordinate systems • local coordinates not an inertial frame • ‘ficticious’ forces: • centrifugal • Coriolis 3 Rotating coordinate systems 4 Rotating coordinate systems xkcd.com 5 Coriolis effect H Coriolis 300 m s-1 L • • • • pressure gradient L 460 m s-1 tendency to turn right in N hemisphere to observer moving with Earth, appears as virtual force pressure gradient balances Coriolis & centrifugal forces at altitude, flow follows isobars around high/low pressure 6 Buys-Ballot’s law H Coriolis 300 m s-1 L pressure gradient L • with the wind on your back, in the N hemisphere, the low pressure is on the left 460 m s-1 Low High 7 Geostrophic wind GEOSTROPHIC WIND • closer isobars → higher Coriolis force → stronger wind • isobars: pressure contours (4 hPa) • cold/warm fronts divide air masses 8