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.
300 fundamentals
A travelling wave carries energy while the medium's particles oscillate around equilibrium. Its speed is v = f lambda; the source fixes frequency, while the medium fixes wave speed, so wavelength adjusts when the medium changes.
Memory trick: source keeps frequency; medium sets speed; wavelength adapts.
A charge moving in magnetic field feels q(v x B). The force is perpendicular to both velocity and field, so a magnetic field changes direction of motion but does no work and cannot change speed by itself.
Memory trick: only the perpendicular velocity component bends.
Two sources are coherent if they keep a constant phase difference — a must for a steady interference pattern.
Memory trick: stable fringes need one source split in two (constant phase).
The opposition a capacitor (Xc = 1/ωC) or inductor (XL = ωL) offers to AC — frequency-dependent, unlike resistance.
Memory trick: reactance changes with frequency; resistance doesn't.
Forward bias (p to +, n to −) lowers the junction barrier and lets current flow; reverse bias widens the depletion region and blocks it.
Memory trick: a diode is a one-way valve for current — forward on, reverse off.
“Telling someone you walked 5 km is a scalar; telling them 5 km north is a vector — direction changes everything.”
A scalar has only magnitude (mass, time, speed); a vector has magnitude AND direction (displacement, velocity, force).
Memory trick: If direction matters, it's a vector.
“Cruise control aims for uniform motion; city traffic is relentlessly non-uniform.”
Uniform motion covers equal distances in equal times (zero acceleration); non-uniform motion does not.
Memory trick: Constant velocity = uniform.
“The same push gives a shopping trolley a big shove but barely moves a truck.”
The net force equals the rate of change of momentum, and for constant mass F = ma.
F = ma
Memory trick: Force = mass × acceleration.
“Doubling your car's speed quadruples its crash energy — why speed limits matter so much.”
Energy of motion, KE = ½mv² — it grows with the square of speed.
KE = ½mv²
Memory trick: Speed doubles → KE quadruples.
“A tightrope walker's long pole spreads mass out, making rotation sluggish and balance easier.”
Rotational 'mass' — resistance to angular acceleration; depends on how mass is distributed about the axis.
I = Σmr²
Memory trick: Mass far from axis counts a lot (distance squared).
“You'd weigh slightly less on a mountaintop than at sea level.”
g = GM/R² at a planet's surface; it weakens with altitude and depth.
g = GM/R²
Memory trick: g depends on the planet, not on you.
“A car hydraulic lift raises tonnes with a gentle push — pressure shared across a big piston.”
Pressure applied to an enclosed fluid is transmitted equally in all directions.
Memory trick: Small force, big area → big force.
“Steel has a huge Young's modulus — that's why it barely stretches under load.”
A measure of a solid's stiffness: stress divided by longitudinal strain.
Y = stress/strain
Memory trick: Higher modulus = stiffer material.
“Grandfather clocks keep time using a pendulum of a fixed length.”
A simple pendulum's period depends only on length and g, not on mass or (small) amplitude.
T = 2π√(L/g)
Memory trick: Only length & g matter.
“Gaps are left between railway rails so they don't buckle on hot days.”
Most materials expand when heated as molecules vibrate more and spread apart.
Memory trick: Hotter → bigger.
“The 'invisible reach' of a charge that pushes other charges around.”
Force per unit positive charge; field lines point away from + and toward − charges.
E = F/q
Memory trick: Field lines never cross.
“A long thin extension cord heats up more than a short thick one.”
Resistance R = ρL/A grows with length and falls with cross-sectional area.
R = ρL/A
Memory trick: Long & thin → more resistance.
“Wiggle a magnet near a coil and you generate electricity — the basis of every generator.”
A changing magnetic flux induces an EMF, EMF = −dΦ/dt.
EMF = −dΦ/dt
Memory trick: Only a CHANGING flux induces.
“A straw looks broken at the water's surface because light bends as it exits.”
Light bends at a boundary: n₁ sinθ₁ = n₂ sinθ₂.
n₁sinθ₁ = n₂sinθ₂
Memory trick: Into denser medium → bends toward normal.
“Bluer light carries more energetic photons than red — which is why UV can burn your skin.”
Light comes in quanta of energy E = hf = hc/λ.
E = hf
Memory trick: Higher frequency → more energetic photon.
“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.
A frequent error is writing both components positive even when the arrow points left or downward. In reality, A vector is one arrow, but we may replace it by perpendicular x- and y-parts that together produce exactly the same effect. If the vector A makes angle theta with +x, then A_x = A cos(theta) and A_y = A sin(theta); signs come from the actual directions, not from the formula.
Memory trick: draw the arrow first; cosine sits beside the marked angle, sine sits opposite it, then assign signs.
A frequent error is using heat and temperature as if they were the same physical quantity. In reality, Temperature tells how hot a body is and sets the direction of heat flow; heat is energy transferred because of a temperature difference. A bucket of warm water can contain more thermal energy than a cup of hotter water.
Memory trick: temperature decides direction; heat is energy in transit.
A frequent error is imagining pressure as a stored substance inside the gas. In reality, Gas pressure comes from molecular collisions with container walls. Each collision changes molecular momentum; the wall experiences the equal and opposite momentum transfer spread over time and area.
Memory trick: more frequent or harder wall hits mean higher pressure.