Mechanics and thermodynamics (algebra based):
The metric system: the seven base units. Metric prefixes. Meter, kilogram, second. Frames of reference. Scalars and vectors. Kinematics in one dimension. Position, displacement, velocity, acceleration. Speed vs. velocity. Constant velocity motion, constant acceleration motion. Instantenous velocity, average velocity. Free fall. Galileo's free fall experiment.
Reference frame, relative motion. Galilean velocity addition. Kinematics in two dimensions. Projectile motion, initial velocity. Height and range of projectile motion. The kinematics of circular motion. Centripetal or center-seeking acceleration.
Dynamics. Force, net force. The three laws of Newton: 1st law: the Law of Inertia. 2nd law: a = F/m. 3rd law: action-reaction principle. The four fundamental forces of Nature. Field forces and contact forces. Weight, tension, normal force. Friction: kinetic and static friction. Atwood machine. Inclines: frictionless and frictional. Air drag. The dynamics of circular motion.
Force, displacement, work. Scalar product of two vectors. Work and power. Units: joule, watt, calorie, horsepower. Energy: the ability to do work. The Principle of Energy Conservation. Forms of energy: mechanical and non-mechanical energies. Kinetic energy. The work-energy theorem. Gravitational potential energy. Spring, Hooke's law. The potential energy of the spring. Conservative and dissipative forces. Energy balance. Isolated vs. open systems. Conservative vs. dissipative systems.
(Linear) momentum and impulse. Conservation of momentum. Impulse-momentum theorem. Applications: bumpers, air bags, cushions. Collisions and interactions. Perfectly elastic and perfectly inelastic collisions. Systems of particles: center of mass vs. center of gravity. Rocket motion, thrust, Tsiolkovsky formula.
Oscillations: simple harmonic motion. Restoring force. Position, velocity and acceleration of SHM. Amplitude. Oscillator and pendulum. Mathematical and physical pendulum. Kinetic and potential energy of SHM. Damped harmonic oscillation. Driven harmonic oscillation. Resonance.
Rotation. Vector product, right hand rule. Torque, force couple. Moment arm. Newton's 2nd law for rotation. Moment of inertia. Parallel axis theorem. Rotational kinetic energy. Rolling vs. sliding, degree of freedom. Angular momentum. Conservation of angular momentum. Precession. Application: gyroscope. Static equilibrum of extended objects. Balanced forces and torques. Bars, bridges, lifting booms, cranes. Simple machines, mechanical advantage.
Gravity. (Inertial frames. Special relativity. 1st postulate: principle of relativity. 2nd postulate: constancy of the speed of light. General relativity: gravitational equivalence principle. Inertial and gravitational mass. Inertial forces: centrifugal force, Coriolis force.) Newton's universal law of gravity: the inverse square law. Gravitational potential energy. The three laws of Kepler. Satellites: 1st and 2nd cosmic speeds. Kinetic, potential and mechanical energy of satellites. Geosynchronous orbit.
Phases: states of matter. Solid, liquid, gas. Density. Elasticity: tension, compression, Young's modulus. Shear, bulk compression, torsion. Pressure, hydrostatic pressure, Pascal's principle. Buoyancy, buoyant force. Archimedes's principle. Fluids. Fluid flow: incompressible vs. compressible, ideal vs. viscous, laminar vs. turbulent, irrotational vs. rotational flow. Bernoulli's principle: conservation of energy. Applicatitons: airplane wings, Venturi effect, curveballs.
Mechanical waves: longitudinal vs. transverse. Speed, wavelength and frequency. Wave equation: wave number and angular velocity. Displacement
and amplitude. Superposition of waves. Interference: constructive and destructive. Reflection of waves: fixed vs. free ends. Speed of sound
and mechanical waves. Intensity vs. sound level: the decibel scale. Hearing threshold, pain threshold. Doppler effect. Shock waves, sonic booms. Mach number, Mach cone. Standing waves. Nodes and antinodes. Musical instruments: string and pipes. Harmonic numbers.
Temperature and thermometers. Temperature scales: Fahrenheit, Celsius, Kelvin. Thermal expansion of solids and liquids. Ideal gas. Gas laws: Boyle-Mariotte, Gay-Lussac, Charles. Universal gas law. Ideal gas law. Regnault constant, Boltzmann constant. Kinetic theory of gases. The micro-macro connection: temperature and RMS speed. The Maxwell-Boltzmann distribution of molecular speeds.
Heat, heat capacity, specific heat, molar heat (constant volume, constant pressure). Degree of freedom of molecules. Phase changes, latent heats: heat of fusion, heat of vaporization. The three ways of heat transfers: conduction, convection, radiation. Black body radiation. Wien's displacement law. Stefan-Boltzmann law.
The laws of thermodynamics. 1st: the equivalence of work and heat. 2nd: the direction of thermodynamic processes. Thermodynamic processes: isothermal, isochoric, isobaric, adiabatic (iso-entropic) and their p-V diagrams. Heat engines, heat pumps, refrigerators. Efficiency and coefficients of performance. Entropy: reduced heat. The thermodynamics of life on Earth.