Fundamentals
The core facts every aspirant should own — each a titled nugget with a real-world story, the concept in plain words, and a memory trick. Works even when the internet doesn't.
1,200 fundamentals
“The same gravity that drops an apple keeps the Moon endlessly 'falling' around the Earth.”
Orbital velocity keeps a satellite in a circular orbit; escape velocity (√2 times larger) lets it leave gravity forever.
“The same gravity that drops an apple keeps the Moon endlessly 'falling' around the Earth.”
Above the surface g ∝ 1/(R+h)²; below the surface g decreases roughly linearly to zero at the centre.
“The same gravity that drops an apple keeps the Moon endlessly 'falling' around the Earth.”
Weight is the gravitational force experienced (mg); in free fall the sensation of weight vanishes even though gravity still acts.
“The same gravity that drops an apple keeps the Moon endlessly 'falling' around the Earth.”
Mgh is only valid near the surface; use −GMm/r otherwise.
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
A frequent error is getting the sign of W wrong (work done by vs on the gas). In reality, energy conservation for gases: ΔU = Q − W, where W is work done BY the gas.
Memory trick: heat in is +Q; work done by the gas is +W and lowers ΔU.
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
The total microscopic energy of a system; for an ideal gas it depends only on temperature.
Memory trick: same temperature → same internal energy for an ideal gas.
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
A frequent error is thinking internal energy depends on pressure or volume for an ideal gas. In reality, the total microscopic energy of a system; for an ideal gas it depends only on temperature.
Memory trick: same temperature → same internal energy for an ideal gas.
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
A frequent error is believing you can fully convert heat into work in a cycle. In reality, heat flows spontaneously from hot to cold, and no engine can be 100% efficient.
Memory trick: some heat must always be dumped to a cold reservoir.
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
Gas pressure comes from molecular collisions, and average molecular KE is proportional to absolute temperature.
Memory trick: always convert temperature to Kelvin for PV=nRT.
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
A frequent error is using Celsius instead of Kelvin in gas relations. In reality, gas pressure comes from molecular collisions, and average molecular KE is proportional to absolute temperature.
Memory trick: always convert temperature to Kelvin for PV=nRT.
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
First law: change in internal energy from heat and work. Use it when W is work done by the gas.
ΔU = Q − W
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
Ideal-gas equation of state. Use it when the gas behaves ideally.
PV = nRT
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
Mayer's relation between molar heat capacities. Use it when one mole of ideal gas.
C_p − C_v = R
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
Efficiency of a heat engine. Use it when a cyclic engine between two reservoirs.
η = 1 − Q_c/Q_h
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
Isothermal keeps temperature constant (ΔU=0, heat exchanged); adiabatic exchanges no heat (Q=0, temperature changes).
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
Heat is energy in transit due to a temperature difference; temperature measures the average kinetic energy of molecules.
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
C_p (constant pressure) exceeds C_v (constant volume) because at constant pressure some heat also does expansion work.
“A pressure cooker is thermodynamics in your kitchen — trapping steam to raise pressure and temperature.”
Heat is transferred energy; temperature is a state variable — they are not the same.
“A swing, a guitar string and an earthquake all speak the same language: oscillations.”
A frequent error is assuming every back-and-forth motion is SHM. In reality, oscillation where the restoring force is proportional to and opposite the displacement, F = −kx.
Memory trick: only a linear restoring force (∝ −x) gives true SHM.
“A swing, a guitar string and an earthquake all speak the same language: oscillations.”
T = 2π√(L/g) — it depends on length and gravity, not on mass or (small) amplitude.
Memory trick: only length and g change a pendulum's period.
“A swing, a guitar string and an earthquake all speak the same language: oscillations.”
A frequent error is thinking a heavier bob swings with a different period. In reality, T = 2π√(L/g) — it depends on length and gravity, not on mass or (small) amplitude.
Memory trick: only length and g change a pendulum's period.
“A swing, a guitar string and an earthquake all speak the same language: oscillations.”
A wave transfers energy and momentum through a medium without transporting the medium itself.
Memory trick: the particles only oscillate in place; the disturbance moves.
“A swing, a guitar string and an earthquake all speak the same language: oscillations.”
A frequent error is thinking the particles travel along with the wave. In reality, a wave transfers energy and momentum through a medium without transporting the medium itself.
Memory trick: the particles only oscillate in place; the disturbance moves.
“A swing, a guitar string and an earthquake all speak the same language: oscillations.”
A frequent error is adding the frequencies instead of subtracting. In reality, the slow throbbing when two close frequencies superpose; beat frequency = |f₁ − f₂|.
Memory trick: beats let musicians tune by ear — zero beats means in tune.