Mechanics and Relativity
Introduction: What is Physics? The nature of physical understanding, the role of mathematical models.
Equilibrium: Forces as influences tending to produce motion. Empirical scale of force. Forces as vectors. Equilibrium as zero sum of forces. Action and reaction, equal and opposite in Equilibrium. Contact forces and friction. Pressure, shear force. Hydrostatics. P the same in all directions in a fluid. Upthrust, proof of Archimedes principle. Turning moment in 2D. Law of lever. Equilibrium of rigid body in 2D, examples. Centre of mass. Finding CofM by integration. Work as scalar product, potential energy. Graphs of PE, stable and unstable equilibrium, examples.
Newton's laws of motion : Aristotelean idea of F proportional to v. Galilean alternative, Newton's first law. Newton's second law, inertial mass. Units and dimensions. Uniform acceleration (e.g. gravity near the Earth's surface). Kinetic energy, conservation of energy. Newton's third law. Momentum, impulse, conservation of momentum. Galilean transformations. Zero momentum frame, elastic and inelastic collisions.
Special Relativity: Michelson-Morley experiment. Einstein's postulates. Lorentz Transformations, simultaneity, time dilation, proper time, length contraction. Twin paradox, causality. Experimental evidence. Velocity transformation and velocity addition; aberration of light, Doppler effect. Relativistic momentum and energy, E=g mc2, conservation of energy and momentum, E-p invariant.
Circular orbits, gravity and rotations: Circular motion, centripetal force, examples including conical pendulum. Orbits, angular momentum in 2D, conservation. Kepler's 2nd law, Kepler's 3rd law and Newton's inverse square law for gravity. Simple elliptical orbits. Gravitational potential. Proof of Gauss' law. Gravity as conservative field. Principle of superposition. Use of Gauss in spherical and plane symmetry. Angular momentum of rigid bodies about a fixed axis. Linear and angular motions, moment of inertia I, angular momentum, rotational kinetic energy. Calculation of I, parallel and perpendicular axis theorems. Compound pendulum. Angular impulse, collisions involving rotation about a fixed axis. Angular momentum vector in 3-D, precession.
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