T = 2π√(m/k)

“A swing, a guitar string and an earthquake all speak the same language: oscillations.”

Period of a mass on a spring. Use it when ideal spring, small oscillations.

T = 2π√(m/k)

T = 2π√(L/g)

“A swing, a guitar string and an earthquake all speak the same language: oscillations.”

Period of a simple pendulum. Use it when small angular amplitude.

T = 2π√(L/g)

v = fλ

“A swing, a guitar string and an earthquake all speak the same language: oscillations.”

Wave speed equals frequency times wavelength. Use it when any wave.

v = fλ

f_beat = |f₁ − f₂|

“A swing, a guitar string and an earthquake all speak the same language: oscillations.”

Number of beats heard per second. Use it when two nearly-equal frequencies.

f_beat = |f₁ − f₂|

transverse wave vs longitudinal wave

“A swing, a guitar string and an earthquake all speak the same language: oscillations.”

In a transverse wave particles move perpendicular to the wave (light, string); in a longitudinal wave they move along it (sound).

amplitude vs frequency

“A swing, a guitar string and an earthquake all speak the same language: oscillations.”

Amplitude sets the loudness/energy of a wave; frequency sets its pitch/colour.

mechanical wave vs electromagnetic wave

“A swing, a guitar string and an earthquake all speak the same language: oscillations.”

Mechanical waves need a medium (sound); electromagnetic waves (light) travel through vacuum.

Myth: Pendulum period depends on mass

“A swing, a guitar string and an earthquake all speak the same language: oscillations.”

It depends only on length and g — mass cancels out.

Coulomb's law — common mistake

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

A frequent error is ignoring that like charges repel and unlike attract when assigning direction. In reality, the force between two point charges, F = kq₁q₂/r², along the line joining them.

Memory trick: it mirrors gravitation but can be attractive OR repulsive.

Electric field — common mistake

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

A frequent error is treating field (a vector) and potential (a scalar) as the same thing. In reality, the force per unit positive charge, E = F/q; field lines point away from positive charges.

Memory trick: field lines never cross and start on + and end on − charges.

Electric potential — common mistake

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

A frequent error is thinking zero field means zero potential (or vice versa). In reality, the work done per unit charge to bring a charge from infinity to a point, V = kQ/r.

Memory trick: potential is a scalar — just add contributions with sign, no directions.

Capacitance — common mistake

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

A frequent error is forgetting a dielectric increases capacitance. In reality, a capacitor's ability to store charge per volt, C = Q/V; for parallel plates C = ε₀A/d.

Memory trick: closer, larger plates (and a dielectric) store more charge.

F = kq₁q₂/r²

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

Coulomb force between point charges. Use it when point charges in vacuum.

F = kq₁q₂/r²

E = kQ/r²

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

Field of a point charge at distance r. Use it when point charge.

E = kQ/r²

V = kQ/r

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

Potential of a point charge. Use it when point charge, zero at infinity.

V = kQ/r

U = ½CV²

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

Energy stored in a charged capacitor. Use it when capacitance C at voltage V.

U = ½CV²

electric field vs electric potential

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

Field is a vector (force per charge, N/C); potential is a scalar (energy per charge, volts) — field points from high to low potential.

capacitors in series vs capacitors in parallel

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

In series the charge is the same and 1/C adds (total C smaller); in parallel the voltage is the same and C adds (total C larger).

conductor vs insulator

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

A conductor has free charges that move easily; an insulator holds its charges in place.

Myth: Field and potential are identical

“Rub a balloon on your hair and it sticks to the wall — electrostatics you can feel.”

E is a vector and V a scalar; E can be zero where V isn't (inside a charged shell) and vice versa.

Ohm's law — common mistake

“Every light you switch on is Ohm's law quietly at work.”

A frequent error is assuming every component is ohmic (a diode or bulb filament is not). In reality, for many conductors V = IR at constant temperature.

Memory trick: Ohm's law is a property of some materials, not a universal rule.

Resistance and resistivity

“Every light you switch on is Ohm's law quietly at work.”

R = ρL/A: resistance grows with length and shrinks with cross-section; resistivity ρ is the material's own property.

Memory trick: a long thin wire resists more than a short thick one of the same material.

Resistance and resistivity — common mistake

“Every light you switch on is Ohm's law quietly at work.”

A frequent error is confusing resistance (depends on shape) with resistivity (depends only on material and temperature). In reality, R = ρL/A: resistance grows with length and shrinks with cross-section; resistivity ρ is the material's own property.

Memory trick: a long thin wire resists more than a short thick one of the same material.

Series and parallel resistors

“Every light you switch on is Ohm's law quietly at work.”

In series the current is the same and resistances add; in parallel the voltage is the same and 1/R values add.

Memory trick: parallel resistance is always less than the smallest branch.