Moving-coil galvanometer

“The needle behind old analogue meters is a galvanometer.”

Detects small currents by the turning of a coil in a magnetic field.

Memory trick: Current → coil deflection.

Diamagnetic, paramagnetic, ferromagnetic

“Iron leaps to a magnet; water is faintly pushed away.”

Materials are weakly repelled, weakly attracted, or strongly attracted by magnetic fields.

Memory trick: Ferromagnets are strongly attracted.

Self-induction

“It's why a switch can spark as a coil resists sudden change.”

A changing current in a coil induces an opposing EMF in itself.

Memory trick: Coil opposes its own change.

Electromagnetic waves

“Light, radio and X-rays are the same wave at different frequencies.”

Oscillating electric and magnetic fields travelling at the speed of light, needing no medium.

c = 3×10⁸ m/s

Memory trick: No medium needed.

EM spectrum order

“Your remote (infrared) and a dentist's X-ray are cousins on one spectrum.”

From long to short wavelength: radio, microwave, infrared, visible, UV, X-ray, gamma.

Memory trick: Longer wave = lower energy.

X-rays

“That's why a fracture shows up clearly on an X-ray.”

High-energy EM radiation that penetrates soft tissue but not bone.

Memory trick: Penetrate flesh, stopped by bone.

Binding energy per nucleon

“Iron is the most stable nucleus — the ashes of stellar fusion.”

Peaks around iron; nuclei lighter or heavier release energy by fusing or splitting toward it.

Memory trick: Iron sits at the peak.

Nuclear force

“It overpowers the electric repulsion that would otherwise blow the nucleus apart.”

An extremely strong but short-range force binding protons and neutrons together.

Memory trick: Strong but very short-range.

LED

“Efficient LEDs now light homes worldwide, sipping a fraction of old-bulb power.”

A light-emitting diode gives out light when current passes in forward bias.

Memory trick: Forward bias → light.

Capacitors in series and parallel

“It's the mirror image of the resistor rules.”

In parallel capacitances add; in series the reciprocals add (like resistors reversed).

Memory trick: Parallel adds C; series adds 1/C.

Dimensional analysis

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

Expressing every quantity in powers of mass (M), length (L) and time (T) so you can check or derive relations.

Memory trick: use it as a quick error-check and to convert units, not to fix constants.

Dimensional analysis — common mistake

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

A frequent error is thinking a dimensionally-correct equation must be numerically correct — dimensionless constants (like 2 or π) are invisible to it. In reality, expressing every quantity in powers of mass (M), length (L) and time (T) so you can check or derive relations.

Memory trick: use it as a quick error-check and to convert units, not to fix constants.

Significant figures

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

The digits in a measurement that actually carry meaning, reflecting the instrument's precision.

Memory trick: in multiply/divide, the result keeps the least number of significant figures.

Significant figures — common mistake

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

A frequent error is keeping more digits in the answer than the least-precise measurement allows. In reality, the digits in a measurement that actually carry meaning, reflecting the instrument's precision.

Memory trick: in multiply/divide, the result keeps the least number of significant figures.

Errors in measurement

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

Absolute error = |measured − true|, relative error = absolute/true, percentage error = relative × 100.

Memory trick: in products/quotients, percentage errors simply add up.

Errors in measurement — common mistake

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

A frequent error is mixing up accuracy (closeness to the true value) with precision (repeatability). In reality, absolute error = |measured − true|, relative error = absolute/true, percentage error = relative × 100.

Memory trick: in products/quotients, percentage errors simply add up.

Least count

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

The smallest value an instrument can reliably read — e.g. 0.01 mm for a screw gauge.

Memory trick: always note and subtract the zero error before recording a reading.

Least count — common mistake

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

A frequent error is forgetting the zero-error correction of a vernier or screw gauge. In reality, the smallest value an instrument can reliably read — e.g. 0.01 mm for a screw gauge.

Memory trick: always note and subtract the zero error before recording a reading.

Δ(AB)/AB = ΔA/A + ΔB/B

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

The fractional error of a product equals the sum of fractional errors. Use it when combining independently-measured quantities.

Δ(AB)/AB = ΔA/A + ΔB/B

accuracy vs precision

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

Accuracy is how close a reading is to the true value; precision is how repeatable your readings are — you can be precise but inaccurate.

fundamental quantities vs derived quantities

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

Fundamental quantities (length, mass, time…) are defined independently; derived quantities (speed, force…) are built from them.

systematic error vs random error

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

Systematic errors are consistent and one-directional (fixable by calibration); random errors scatter both ways (reduced by averaging).

Myth: Rounding too early

“Engineers sanity-check rocket equations by their units first — a units mix-up famously doomed a real Mars probe.”

Round only at the final step, never in the middle of a calculation.

Instantaneous velocity

“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”

The velocity at a single instant — the slope of the position–time graph at that point.

Memory trick: read it as the tangent slope of the x–t graph.