Simple Harmonic Motion

The physics of anything that vibrates about a fixed point: the defining condition a = −ω²x and its sinusoidal solution, displacement, velocity and acceleration with their graphs and phase relations, the exchange of kinetic and potential energy, the periods of the simple pendulum, the mass–spring system and a liquid in a U-tube, and how two simple harmonic motions of the same frequency add.

2

Damped and Forced Oscillations

What happens to real oscillators: damping forces and the light, critical and heavy regimes, the exponential loss of amplitude and energy, the quality factor, and forced oscillations driven at any frequency, with the energy balance of the steady state, resonance, and its uses and dangers in machines, bridges, buildings and instruments.

3

Propagation of Mechanical Waves

How disturbances travel through matter: transverse and longitudinal waves and the quantities that describe them, wave speed in strings, solids and gases, the equation of a progressive wave and phase difference, the formation and equation of stationary waves with their nodes and antinodes, and the harmonics of a vibrating string, from the sonometer to the inanga.

4

Fluid Mechanics

Fluids at rest and in motion: how pressure grows with depth and how U-tube manometers measure it, surface tension, excess pressure in drops and bubbles, capillary rise, streamline flow and the continuity equation, Bernoulli's principle and the Venturi meter, viscosity, Stokes' law and terminal velocity, with applications from Lake Kivu's deep gas to aircraft wings and muddy rivers.

5

Motion in Orbits

Gravity from the apple to the planets: Newton's law of gravitation and the gravitational field, how g changes above and below the Earth's surface, gravitational potential energy and escape, Kepler's three laws and their test with planetary data, the first, second and third cosmic velocities, and satellites in low, polar and geostationary orbits, including Rwanda's own.

6

Atomic Models

How the picture of the atom was built from experiment: Thomson's plum pudding, Rutherford's alpha-scattering experiment and the nuclear atom, Bohr's model of hydrogen with its quantised orbits and energies, energy levels and the line spectra they produce, and thermionic emission, cathode rays and the measurement of the electron's charge-to-mass ratio, with their uses.

7

Wave and Particle Nature of Light

Why hot bodies glow as they do and how Planck's quantum explained it; photons, the photoelectric effect and its uses; Compton scattering and other photon interactions; and de Broglie's matter waves, which show that electrons diffract like light.

8

Signals and Communication Systems

How a communication system carries information: analogue and digital signals, attenuation and noise in decibels, sampling and quantisation, AM and FM modulation, radio propagation and receivers, cellular mobile networks, and how communication technology has evolved from the telegraph to 5G.

9

Magnetic Field and Magnetic Forces

Where magnetic fields come from and how to calculate them for a straight wire, a loop and a solenoid; the force on a moving charge and on a current, magnetic flux and Gauss's law for magnetism; circular motion of charged particles, the velocity selector, Thomson's e/m experiment and the mass spectrometer; and the torque on a coil that drives the DC motor.

10

Introduction to the Special Theory of Relativity

Frames of reference and the Galilean transformation; why the constant speed of light broke classical physics; Einstein's two postulates and the relativity of simultaneity; time dilation and length contraction, with muons and GPS as evidence; and relativistic momentum, energy and the equivalence of mass and energy, E = mc².

11

Interference and Diffraction of Light

Light as an electromagnetic wave and the conditions for two light waves to interfere; Young's double-slit experiment and the fringe-spacing formula; the cos² intensity distribution of a fringe pattern; and diffraction by a single slit, by a circular aperture (the limit of resolution) and by a diffraction grating.

Units