Logic gates

“Every app you use is, deep down, billions of these tiny switches.”

Digital electronics is built from AND, OR and NOT gates acting on 1s and 0s.

Memory trick: Computers think in AND/OR/NOT.

Vernier calliper

“It measures a coin's thickness far better than any ruler.”

A vernier scale lets you read lengths to 0.1 mm by aligning scale marks.

Memory trick: Read main + vernier coincidence.

Screw gauge least count

“It gauges a hair's width — about 0.05 mm.”

A screw gauge measures to 0.01 mm using a circular scale on a fine screw.

Memory trick: Least count = pitch ÷ divisions.

Systematic vs random error

“A miscalibrated scale is systematic; a shaky hand is random.”

Systematic errors are consistent (fixable by calibration); random errors scatter (reduced by averaging).

Memory trick: Calibrate vs average.

Conical pendulum

“A tetherball loops around the pole as a conical pendulum.”

A mass whirling in a horizontal circle on a string traces a cone; the horizontal string component supplies the centripetal force.

Memory trick: String tension turns it.

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.

Elastic potential energy

“A drawn bow stores the energy that launches the arrow.”

Energy stored in a stretched or compressed spring, ½kx².

PE = ½kx²

Memory trick: Stored in the stretch.

Coefficient of restitution

“A super-ball has e near 1; wet clay has e near 0.”

Measures a collision's bounciness: 1 for perfectly elastic, 0 for perfectly inelastic.

Memory trick: e = 1 bouncy, e = 0 dead.

Stationary waves

“A plucked guitar string vibrates as a stationary wave.”

Two identical waves travelling opposite ways superpose into fixed nodes and antinodes.

Memory trick: Nodes stay still, antinodes swing.

Harmonics and overtones

“Harmonics give each instrument its unique timbre.”

A string or pipe vibrates at a fundamental frequency and whole-number multiples (harmonics).

Memory trick: Multiples of the fundamental.

Organ pipes

“It's why a flute and a closed pipe of the same length sound different.”

An open pipe supports all harmonics; a closed pipe only odd harmonics.

Memory trick: Closed pipe = odd harmonics only.

Intensity and loudness

“Step twice as far from a speaker and the sound drops to a quarter.”

Sound intensity falls with the square of distance from the source.

Memory trick: Inverse-square with distance.

Mirror formula

“It predicts exactly where a mirror will form your image.”

For spherical mirrors, 1/v + 1/u = 1/f.

1/v + 1/u = 1/f

Memory trick: Note the sign convention.

Magnification

“A magnifying glass gives magnification greater than one.”

Ratio of image size to object size; sign shows upright or inverted.

Memory trick: m = −v/u for mirrors.

Power of a lens

“Your spectacle prescription is quoted in dioptres.”

Optical power P = 1/f (in dioptres); positive for convex, negative for concave.

P = 1/f

Memory trick: Power = 1/f (metres).

Myopia and hypermetropia

“Glasses simply nudge the focus back onto the retina.”

Short sight (myopia) is corrected by concave lenses; long sight (hypermetropia) by convex lenses.

Memory trick: Myopia → concave; hypermetropia → convex.

Scattering of light

“Sunlight scatters blue across the sky and leaves red for dusk.”

Shorter wavelengths scatter more, making the sky blue and sunsets red.

Memory trick: Blue scatters most.

Gauss's law

“It turns messy field calculations into elegant symmetry arguments.”

The electric flux through a closed surface equals the enclosed charge divided by ε₀.

Φ = q/ε₀

Memory trick: Flux ∝ charge enclosed.

Electric dipole

“A water molecule behaves as a tiny electric dipole.”

Two equal and opposite charges a small distance apart; its field falls off as 1/r³.

p = q×2a

Memory trick: Dipole field ∝ 1/r³.

Drift velocity

“Electrons crawl, yet the light comes on instantly because the field spreads at light speed.”

The slow average velocity of electrons in a conductor under a field (~mm/s).

Memory trick: Signal fast, electrons slow.

Wheatstone bridge

“It's the precision scale of the electrical world.”

A four-resistor network that finds an unknown resistance when balanced (no galvanometer current).

Memory trick: Balanced → no bridge current.

Potentiometer

“Unlike a voltmeter, it doesn't disturb the circuit it measures.”

Measures EMF without drawing current, so it reads a cell's true voltage.

Memory trick: No current drawn = true EMF.

Biot–Savart law

“It's the building block for the field of any wire shape.”

Gives the magnetic field produced by a small current element.

Memory trick: Current element → tiny field.

Solenoid field

“Electromagnets in scrapyards are just powerful solenoids.”

A long current-carrying coil produces a nearly uniform field inside, like a bar magnet.

B = μ₀nI

Memory trick: Uniform field inside.