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 runner’s split-second speed on a stopwatch is not the same as the average speed over the whole lap.”
Average velocity = total displacement ÷ total time, while instantaneous velocity is the limit as the time interval approaches zero. Using Δs/Δt for a finite interval gives the average, not the instant.
Memory trick: Avg = Δs/Δt; instant = limit Δt→0
“A hockey puck glides on smooth ice, staying at constant speed until a stick hits it—showing inertia.”
Inertia is the resistance of any mass to a change in its state of rest or uniform motion, as stated in Newton’s first law. It is not a force; it is proportional to mass. A frequent error is to think a force is needed to keep an object moving; only a net external force changes its motion.
Memory trick: Inertia ∝ mass, no force needed to stay moving.
“Carrying a heavy bag straight across a room does no work against gravity because the force is vertical while displacement is horizontal.”
When the applied force is perpendicular to the displacement, cosθ = 0, so work is zero. Students often count the effort of holding a weight as work, but work measures energy transferred, not mere effort. Remember: only the force component along the motion does work.
Memory trick: Perp force → cos90°=0 → W=0
“A bowling ball rolling down the lane carries both forward speed and spin, giving it extra kinetic energy.”
A rolling object has translational kinetic energy ½mv² and rotational kinetic energy ½Iω². Both must be added for the total kinetic energy. A frequent slip is to count only the translational part or to misuse v = ωr for a slipping case.
Memory trick: KE = ½mv² + ½Iω² → ‘half m v² plus half I ω²’
“A satellite 10 Rₑ from Earth has PE = –GMm/(10Rₑ), far below the zero set at infinity.”
Gravitational potential energy of a mass m at distance r from Earth’s centre is U = –GMm/r, zero at infinity. Near Earth this reduces to mgh, but for satellites the –GMm/r form must be used. Mistake: applying mgh at large r.
Memory trick: PE negative, zero at ∞; use –GMm/r.
“Airplane wings generate lift as air moves faster over the curved top, creating lower pressure there.”
Bernoulli’s equation states P + ½ρv² + ρgh = constant along a streamline for steady, non-viscous, incompressible flow. Hence, where the fluid speed is higher the pressure is lower. Misuse occurs when height changes are ignored or when the flow is viscous or turbulent.
P + ½ρv² + ρgh = constant
Memory trick: Fast = low pressure (Bernoulli).
“When you pull a rubber tube, it gets thinner; the ratio of that thinning to the stretch is the Poisson ratio.”
Poisson’s ratio ν = –(lateral strain)/(longitudinal strain). The negative sign makes ν positive for most materials, which contract laterally when stretched longitudinally. Typical metals have ν ≈ 0.3; ν cannot exceed 0.5 for isotropic elastic solids.
Memory trick: ν = –Δwidth/Δlength
“A flute (open at both ends) can play every note, while a clarinet (closed at one end) skips even notes.”
Open pipe: λ = 2L/n → all integer harmonics. Closed pipe: λ = 4L/(2n-1) → only odd harmonics. The error is applying the open-pipe formula to a closed pipe, giving a nonexistent even harmonic.
Memory trick: Closed = odd only; Open = all
“A gas compressed in a piston feels hotter, but its internal energy rise is due to temperature increase, not pressure itself.”
In an ideal gas internal energy is a function of temperature alone; pressure or volume changes do not affect U directly. Assuming ΔU ∝ ΔP or ΔV is a frequent error. Remember: if temperature stays the same, ΔU = 0.
Memory trick: ΔU = 0 if T constant (ideal gas)
“Climbing a hill feels the height (potential) while wind blowing shows direction (electric field) – one is scalar, the other vector.”
Electric field E is a vector defined as force per unit positive charge, E = F/q, and points from positive to negative charges; electric potential V is a scalar, the work per unit charge, V = -∫E·dl. Trap: using V where E is needed, or treating E as a scalar.
Memory trick: E = arrow, V = height – different types.
“A thin straw sips slower than a thick pipe; similarly, thin wire has higher resistance than a thick one.”
Resistance R = ρ L/A; ρ is the material’s intrinsic resistivity, unchanged by shape. Increasing length raises R, increasing cross-section lowers R. The exam pitfall is mixing up resistivity (material property) with resistance (geometric). Cutting a wire changes R but not ρ.
Memory trick: R ∝ L, ∝ 1/A; ρ stays same
“Moving a magnet through a loop is like shaking a bottle; the liquid (charge) rushes out only while the shaking (flux change) continues.”
Faraday’s law: a changing magnetic flux Φ through a circuit induces an emf ε = –dΦ/dt (or ε = –N dΦ/dt for N turns). Only a change in field strength, area, or orientation produces emf; a steady flux gives none. The negative sign reflects Lenz’s law and is a frequent source of sign errors.
Memory trick: Faraday: EMF = –ΔFlux/Δt → need change, not static.