Centre of mass

“A high-jumper arches so their centre of mass slips under the bar.”

The point where a body's whole mass can be treated as concentrated.

Memory trick: Balance point of mass.

Kepler's third law

“Outer planets crawl; Neptune takes 165 Earth-years for one lap of the Sun.”

The square of a planet's orbital period is proportional to the cube of its orbit radius (T² ∝ r³).

T² ∝ r³

Memory trick: Farther planet → much longer year.

Surface tension

“Water striders walk on ponds and droplets pull into spheres because of surface tension.”

The 'skin' on a liquid caused by cohesive forces pulling surface molecules inward.

Memory trick: Liquids minimise their surface.

Hooke's law and elastic limit

For small deformation within the proportional limit, stress is proportional to strain. Beyond that range the graph need not remain linear, and beyond the elastic limit the body may not recover fully.

Memory trick: straight-line rule only inside the proportional range.

Resonance

“A singer can shatter a wine glass by matching its natural frequency.”

A system driven at its natural frequency oscillates with large amplitude.

Memory trick: Match natural frequency → big swing.

Modes of heat transfer

“A pan heats by conduction, boiling water circulates by convection, and the Sun reaches us by radiation.”

Heat moves by conduction (contact), convection (fluid currents) and radiation (electromagnetic waves).

Memory trick: Contact, currents, rays.

Energy in a capacitor

“Defibrillators store energy in a capacitor and release it to restart a heart.”

A charged capacitor stores energy U = ½CV².

U = ½CV²

Memory trick: Energy grows with voltage squared.

Electric power

“A heater's thick coil and high current turn electrical energy into cosy heat.”

Power dissipated P = VI = I²R = V²/R.

P = VI

Memory trick: P = VI.

AC generator

“Coal, water or wind all do one job: spin a coil to make AC.”

Rotating a coil in a magnetic field induces alternating EMF — the heart of power stations.

Memory trick: Spin a coil → AC.

Convex vs concave lens

“A magnifying glass is convex; glasses for short sight are concave.”

A convex lens converges light (used for magnifying, farsight); a concave lens diverges it (used for nearsight).

Memory trick: Convex converges; concave diverges.

Mass-energy equivalence

“The Sun shines by converting a little mass into enormous energy every second.”

Mass and energy are interchangeable via E = mc².

E = mc²

Memory trick: A tiny mass → huge energy (c² is vast).

Transverse nature

In a plane electromagnetic wave, electric field E and magnetic field B are perpendicular to each other and to the direction of propagation. Their cross-product direction E x B points along energy flow.

Memory trick: E, B and travel direction form three mutually perpendicular axes.

Projectile trajectory

Eliminating time from x = u cos(theta)t and y = u sin(theta)t - gt^2/2 gives a quadratic y(x), so the ideal projectile path is a parabola.

Memory trick: at the top only v_y is zero; v_x is still u cos(theta).

Calorimetry and thermal equilibrium — common mistake

A frequent error is assuming the final temperature is always the simple average. In reality, In an insulated mixture, energy lost by hotter bodies equals energy gained by colder bodies until they reach a common temperature. Use signed heat changes or a clear lost = gained equation, never both conventions at once.

Memory trick: the larger heat capacity pulls the final temperature closer to itself.

Root-mean-square speed

The rms speed is the square root of the mean of v^2, not the ordinary mean speed. It links the molecular picture to measurable pressure and temperature.

Memory trick: molecular-speed formulas always need kelvin.

Equipotential surfaces

Moving a charge along an equipotential surface requires no work by or against the electrostatic field. Electric-field lines cross equipotentials at right angles.

Memory trick: the field may be strong, but it has no component along an equipotential.

Earth as a magnetic field

Locally, Earth's field is described by declination, dip (inclination), and horizontal component. Dip is measured from the horizontal plane, not from the vertical.

Memory trick: declination turns on the map; dip tilts below the horizon.

Hydrogen energy levels

Hydrogen bound-state energies are negative because zero is assigned to a free electron at infinity. Larger n means less negative energy and weaker binding.

Memory trick: n = 1 is deepest; n = infinity is ionised.

Binding energy per nucleon — common mistake

A frequent error is using total binding energy alone to compare nuclear stability. In reality, Binding energy per nucleon measures average tightness of binding. Its curve rises toward iron/nickel and then slowly falls, explaining why both fusion of light nuclei and fission of heavy nuclei can release energy.

Memory trick: compare B/A, not just B.

Graph slope and intercept

A graph can transform a law into y = mx + c. The slope must be calculated with two well-separated points on the best-fit line, not necessarily two raw data points, and it carries units.

Memory trick: slope is Delta y/Delta x with axis scales and units.

Standing waves

Two identical waves travelling oppositely form fixed nodes of zero displacement and antinodes of maximum displacement. A standing wave stores a spatial pattern and has no net energy transport along the medium.

Memory trick: node to next antinode is lambda/4; node to node is lambda/2.

Biot-Savart law

Each current element contributes a magnetic field perpendicular to its direction and the line to the observation point. Integrating these vector contributions gives the field of the whole conductor.

Memory trick: right-hand direction before integration.

Polarisation

Light is a transverse wave, so its vibrations can be restricted to one plane — something only transverse waves can do.

Memory trick: only transverse waves (light) polarise; longitudinal (sound) can't.

Resonance — common mistake

A frequent error is thinking resonance gives maximum impedance. In reality, in a series LCR circuit at f = 1/(2π√LC), XL cancels Xc so impedance is minimum and current is maximum.

Memory trick: at resonance Z = R (smallest), so current peaks — that's radio tuning.