Physics Short Notes — Edexcel AS Level

Physical quantity = numerical value + unit

e.g. mass = 2.5 kg · time = 12 s · current = 0.40 A

SI base quantities (7):

Length (m) · Mass (kg) · Time (s) · Current (A)

Temperature (K) · Amount (mol) · Luminous intensity (cd)

Key derived units:

Force: N = kg m s⁻² (F = ma)

Energy / Work: J = N m

Power: W = J s⁻¹ (P = E / t)

Pressure: Pa = N m⁻² · Charge: C = A s

Potential difference: V = J C⁻¹ · Resistance: Ω = V A⁻¹

Prefixes to memorise:

pico (p) 10⁻¹² · nano (n) 10⁻⁹ · micro (μ) 10⁻⁶ · milli (m) 10⁻³

centi (c) 10⁻² · kilo (k) 10³ · mega (M) 10⁶ · giga (G) 10⁹

Scalars (magnitude only): mass, time, distance, speed, energy, temperature

Vectors (magnitude + direction): displacement, velocity, acceleration, force, momentum

Resolution: horizontal = F cosθ · vertical = F sinθ

Uncertainty

Absolute: write as value ± uncertainty (e.g. 12.5 ± 0.5 cm)

% uncertainty = (absolute uncertainty / value) × 100%

Range method: uncertainty ≈ (max − min) / 2

Mean = sum of readings / number of readings

Combining: add % uncertainties for × or ÷; add absolute for + or −

Practical graphs — what to extract:

displacement–time: gradient = velocity · area not used

velocity–time: gradient = acceleration · area = displacement

force–extension: gradient = spring constant · area = elastic strain energy

Practical method (6-mark answer structure):

1. State independent, dependent and control variables

2. Describe apparatus + how to measure each quantity

3. Repeat readings → calculate mean to reduce random error

4. Plot graph → use gradient / intercept for result

5. Safety hazard + specific precaution

6. Improvement: name instrument with better resolution

Speed (scalar): distance / time · Velocity (vector): displacement / time

Acceleration: rate of change of velocity

a = (v − u) / t unit: m s⁻²

Uniform acceleration = constant acceleration → use SUVAT equations

Always define the positive direction before substituting into SUVAT

SUVAT equations (uniform acceleration only):

v = u + at

s = ut + ½at²

v² = u² + 2as

s = ½(u + v)t

s = displacement (m) · u = initial velocity · v = final velocity

a = acceleration · t = time

Free fall: g = 9.81 m s⁻² downward (use a = −9.81 if up is positive)

Motion graphs:

displacement–time: gradient = velocity (horizontal = stationary)

velocity–time: gradient = acceleration · area under graph = displacement

acceleration–time: area under graph = change in velocity

Curved s–t graph → changing velocity (acceleration present)

Negative gradient on v–t graph → deceleration (or reversed motion)

Straight sloping v–t line → constant (uniform) acceleration

Projectile motion: horizontal and vertical are INDEPENDENT

Horizontal: a = 0 → velocity is constant throughout

Vertical: a = g = 9.81 m s⁻² → use SUVAT

Time of flight controlled by vertical motion only

Range = horizontal velocity × time of flight

Components at launch: uₓ = u cosθ uᵧ = u sinθ

Exam tip: find time using vertical equation, then use it horizontally

Newton's 1st law: object stays at rest or moves at constant velocity unless resultant force ≠ 0

Newton's 2nd law: F = ma (resultant force = rate of change of momentum)

Newton's 3rd law: equal and opposite forces on different objects, same type

N3L pair: same magnitude, opposite direction, same type, different objects

Resultant = 0 → equilibrium · Resultant ≠ 0 → accelerates in that direction

Weight: W = mg g = 9.81 N kg⁻¹ on Earth surface

Normal reaction: perpendicular to surface (not always equal to weight!)

Friction: opposes relative motion or attempted motion between surfaces

Drag / air resistance: resistive force in fluids; increases as speed increases

Terminal velocity:

→ At start: weight > drag → accelerates downward

→ As speed ↑: drag ↑ → acceleration ↓

→ Terminal velocity: weight = drag + upthrust → resultant = 0 → constant speed

Moment of a force: turning effect about a pivot

moment = force × perpendicular distance from pivot

Unit: N m (use perpendicular distance — NOT the sloping distance!)

Principle of moments (rotational equilibrium):

sum of clockwise moments = sum of anticlockwise moments

Centre of gravity: point where the whole weight of an object appears to act

Object is stable if line of action of weight passes through its base

Stability increases with: wider base + lower centre of gravity

To find CoG experimentally: hang from 2+ points, intersect plumb lines

Toppling: object tips when CoG moves outside base → line of action of weight falls outside base

Momentum: p = mv unit: kg m s⁻¹ (vector quantity)

Conservation of momentum:

Condition: no external resultant force (closed / isolated system)

total momentum before = total momentum after

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Choose +ve direction first. Use signs consistently.

Impulse: impulse = FΔt = Δp = mv − mu

Unit: N s = kg m s⁻¹ · Area under force–time graph = impulse

Elastic collision: momentum conserved AND kinetic energy conserved

Inelastic collision: momentum conserved · KE NOT conserved (→ thermal / sound)

Explosion: total initial momentum = 0 → equal and opposite momenta after

Exam trap: KE may not be conserved unless stated as elastic

Work done: W = Fd cosθ unit: J

Work done only by the component of force in the direction of motion

Work is negative if force opposes motion (e.g. friction)

Kinetic energy: Eₖ = ½mv²

Gravitational PE: Eₚ = mgh

Conservation of energy: energy is never created or destroyed — only transferred between stores

Power: rate of energy transfer

P = E / t = W / t unit: W = J s⁻¹

At constant speed: P = Fv

Efficiency:

efficiency = (useful output energy / total input energy) × 100%

or: (useful output power / total input power) × 100%

Energy is scalar — no direction · Power ≠ energy (P = energy per second)

Sankey diagram: thick arrows = large energy · wasted energy shown branching off

Electric charge Q — unit: coulomb (C)

Q = It I = current (A), t = time (s)

Conventional current flows + → − outside the cell (electrons flow −→+)

Kirchhoff's 1st Law: Σ currents into a junction = Σ currents out

Charge is conserved — no charge builds up at a junction

Current I = rate of flow of charge · unit: ampere (A)

I = nqvA n = number density (m⁻³), q = charge per carrier, v = drift velocity, A = area

Ammeter: connected in series · very low resistance

More carriers (larger n) → higher current at same drift velocity

Practical: measuring current

Use a coulombmeter or integrate area under I–t graph to find Q

A larger cross-sectional area wire carries more current

Metal conductors: n ≈ 10²⁸ m⁻³ (very high) → small drift velocity

Potential difference (p.d.) V = energy transferred per unit charge

V = W / Q unit: volt (V = J C⁻¹)

Voltmeter: connected in parallel · very high resistance

EMF ε: energy supplied per unit charge by the source

ε = E / Q E = total energy supplied (J)

Electrical power:

P = IV P = I²R P = V²/R unit: watt (W)

Energy transferred: E = Pt = IVt unit: joule (J)

1 kWh = 3 600 000 J (energy unit on electricity bills)

Higher resistance → more power dissipated at same current (P = I²R)

Resistance R · R = V / I unit: Ω

Ohm's Law: V ∝ I at constant temperature → R is constant

Resistance opposes current; energy transferred to thermal energy

Total power in circuit = ε × I (all power comes from EMF source)

Ohmic resistor: straight line through origin → R constant

Filament lamp: curve (slope decreases) → R increases with temperature

Diode: conducts in forward bias only; threshold ~0.6 V (silicon)

Thermistor (NTC): resistance decreases as temperature rises

LDR: resistance decreases as light intensity increases

Measuring I–V (practical):

Variable resistor (rheostat) in series to vary current

Ammeter in series, voltmeter in parallel with component

Record pairs of I and V; plot graph; gradient = 1/R at that point

For diode: also reverse connections to get reverse-bias section

Resistivity ρ — material property · unit: Ω m

R = ρL / A L = length (m), A = cross-section area (m²)

Longer wire → higher R · Thicker wire → lower R · Different material → different ρ

Rearrange: ρ = RA / L (use this to find resistivity from measurements)

Temperature and resistance:

Metal conductor: R increases with temperature (more lattice vibrations → more scattering)

Thermistor (NTC): R decreases with temperature (more charge carriers freed)

Superconductor: R → 0 below critical temperature T_c

Practical — measuring resistivity of a wire:

Measure diameter d with micrometer (×3, take mean) → A = π(d/2)²

Vary length L with crocodile clips; measure V and I → R = V/I

Plot R vs L → gradient = ρ/A → ρ = gradient × A

Control: same material, same temperature throughout

Internal resistance r: resistance inside the cell itself

ε = V + Ir → V = ε − Ir (terminal p.d.)

Plot V vs I: y-intercept = ε, gradient = −r

Kirchhoff's 2nd Law: sum of EMFs = sum of p.d.s around any closed loop

Series circuit: same current everywhere

R_total = R₁ + R₂ + R₃ …

V divides in ratio of resistances; Q same through each component

Parallel circuit: same p.d. across each branch

1/R_total = 1/R₁ + 1/R₂ + …

Current divides; total current = sum of branch currents

Potential divider:

V_out = V_in × R₂ / (R₁ + R₂)

Replace R₂ with thermistor → V_out changes with temperature

Replace R₂ with LDR → V_out changes with light intensity

Used in sensor circuits; output can feed a comparator or data-logger

Density ρ · ρ = m / V unit: kg m⁻³

Water: ≈ 1000 kg m⁻³ · Air: ≈ 1.2 kg m⁻³ · Aluminium: ≈ 2700 kg m⁻³

Pressure p · p = F / A unit: Pa (= N m⁻²)

Pressure in a fluid at depth h: p = hρg

Pressure acts equally in all directions at the same depth

Upthrust (Archimedes' Principle):

F_upthrust = ρ_fluid × V_submerged × g

Upthrust = weight of fluid displaced

Floating: upthrust = weight of object → object displaces its own weight of fluid

Sinking: weight > upthrust · Rising bubble: upthrust > weight

Practical — density of a liquid:

Weigh empty measuring cylinder; add liquid; record volume from scale

ρ = (mass of liquid) / (volume of liquid)

Density of an irregular solid: use Archimedes — measure upthrust in water

ρ_solid = m_solid × ρ_water / (m_air − m_water) [using readings from balance]

Viscosity: resistance of a fluid to flow · unit: Pa s (= N s m⁻²)

Viscous drag on a sphere (Stokes' Law): F = 6πηrv

η = viscosity, r = radius of sphere, v = velocity

Valid only for laminar (streamline) flow at low speeds

Terminal velocity:

Forces on a falling sphere: weight ↓, upthrust ↑, viscous drag ↑

Terminal velocity when: W = upthrust + drag

At terminal v: acceleration = 0 · resultant force = 0

Larger/denser sphere → higher terminal velocity

Falling-ball viscometry (practical):

Measure time for ball to fall between two marks in glycerol column

Use ruler + stopwatch; allow ball to reach terminal v before timing

At terminal v: η = (W − upthrust) / (6πrv) → solve for η

Control: constant temperature (viscosity decreases as T increases)

Hooke's Law: extension proportional to force if limit of proportionality not exceeded

F = kx k = spring constant (N m⁻¹), x = extension (m)

Springs in series: k_eff = k₁k₂/(k₁+k₂) · Springs in parallel: k_eff = k₁ + k₂

Beyond limit of proportionality: F no longer ∝ x

Elastic behaviour: material returns to original shape when load removed

Plastic behaviour: permanent deformation — does not return to original shape

Elastic strain energy stored: E = ½Fx = ½kx² = area under F–x graph

Loading/unloading curves: if they do not overlap → energy is dissipated (hysteresis)

Practical — spring constant:

Hang masses on spring; record extension x for each added mass

Plot F vs x; gradient = k

Use a ruler clamped alongside spring; read from lowest point of coil

Safety: stand behind clamp; don't exceed elastic limit

Stress σ · σ = F / A unit: Pa (N m⁻²)

Strain ε · ε = x / L₀ (dimensionless ratio)

Young Modulus E · E = σ / ε = FL₀ / Ax unit: Pa

E = gradient of straight-line section of stress–strain graph

Key points on stress–strain graph:

Limit of proportionality: last point where σ ∝ ε

Elastic limit: last point of elastic behaviour

Yield point: sudden large strain at roughly constant stress

UTS (ultimate tensile stress): maximum stress the material can withstand

Fracture point: material breaks

Practical — Young Modulus of a wire:

Long, thin wire (reduces % uncertainty in L and x)

Measure diameter d at 3+ positions with micrometer → A = π(d/2)²

Hang masses; measure extension x with vernier scale or travelling microscope

Plot stress vs strain; gradient = E

Wave speed · v = fλ v (m s⁻¹), f (Hz), λ (m)

Period T · T = 1 / f T (s)

Amplitude A: maximum displacement from equilibrium position

Phase difference: fraction of cycle between two points · in degrees or radians

In phase: phase diff = 0° or 360° (nλ path diff) · Antiphase: 180° ((n+½)λ)

Transverse waves: oscillation ⊥ to direction of propagation (e.g. light, water, strings)

Longitudinal waves: oscillation ∥ to direction of propagation (e.g. sound)

Sound: compressions (high pressure) and rarefactions (low pressure)

EM spectrum (λ decreasing): radio · microwave · IR · visible · UV · X-ray · γ

All EM waves travel at c = 3 × 10⁸ m s⁻¹ in vacuum

Intensity · I = P / A unit: W m⁻²

Intensity ∝ amplitude² · Point source: I ∝ 1/r² (inverse square law)

Practical — speed of sound: use two microphones + datalogger on a metre rule

Measure time delay Δt between microphones separated by d → v = d/Δt

Refractive index n · n = c / v c = speed in vacuum, v = speed in medium

Snell's Law: n₁ sin θ₁ = n₂ sin θ₂

Ray bends towards normal when entering denser medium

Ray bends away from normal when entering less dense medium

Total Internal Reflection (TIR):

Occurs when light travels from dense → less dense medium

Angle of incidence > critical angle C

Critical angle: sin C = 1/n (n = refractive index of dense medium, air outside)

Applications: optical fibres, diamonds, periscope prisms

Polarisation:

Transverse waves can be polarised; longitudinal waves (sound) cannot

Polarisation: oscillation restricted to one plane

Polaroid filter: transmits one direction of oscillation only

Two polaroids at 90°: no light transmitted (crossed polaroids)

Evidence that light is transverse: it can be polarised

Principle of Superposition: resultant displacement = sum of individual displacements

Constructive interference: waves in phase → amplitude adds (path diff = nλ)

Destructive interference: waves antiphase → cancellation (path diff = (n+½)λ)

Coherent sources: same frequency, constant phase difference

Stationary (standing) waves:

Formed by superposition of two identical waves travelling in opposite directions

Node: zero displacement always · Antinode: maximum displacement

Node-to-node distance = λ/2

Fundamental mode: one loop between fixed ends, f₀ = v/2L

Diffraction grating:

d sin θ = nλ d = slit spacing (m), n = order, θ = angle to nth order

Slit spacing d = 1 / (number of lines per metre)

More lines per mm → smaller d → larger θ → wider spread

Use spectrometer to measure θ precisely → calculate λ of light

Young's double slit: fringe spacing

w = λD / s D = distance to screen, s = slit separation, w = fringe width

Bright fringes where path difference = nλ

Single slit diffraction: central maximum is wider and brighter than sides

Diffraction greatest when slit width ≈ λ

Photon energy · E = hf = hc/λ

h = Planck's constant = 6.63 × 10⁻³⁴ J s

Photoelectric effect: photon absorbed by surface electron; electron emitted if E > work function

Work function φ: minimum energy needed to release an electron from the surface

Threshold frequency f₀: minimum frequency for emission · φ = hf₀

Einstein's photoelectric equation:

hf = φ + ½mv²_max

½mv²_max = maximum kinetic energy of emitted electron

Intensity increase → more photons per second → more electrons emitted (if f > f₀)

Intensity does NOT affect KE of electrons; frequency does

Wave-particle duality:

Light: wave (diffraction, interference) and particle (photon/photoelectric)

Electrons also show wave behaviour (electron diffraction)

de Broglie wavelength: λ = h / p = h / mv

Faster/heavier particles → smaller λ → less diffraction

Electron energy levels (line spectra):

Electrons exist in discrete energy levels in an atom

Photon emitted when electron drops to lower level: E = hf = E₁ − E₂

Line spectrum: each element has unique pattern (fingerprint)

Absorption spectrum: dark lines where photons absorbed at specific frequencies

Mechanics

v = u + at · s = ut + ½at² · v² = u² + 2as · s = ½(u+v)t

F = ma · W = mg · F = Δp/Δt · p = mv

Moment = Fd · Torque couple = Fd

W = Fs cosθ · KE = ½mv² · GPE = mgh · P = Fv · efficiency = P_useful/P_input

Electricity

Q = It · V = W/Q · R = V/I · P = IV = I²R = V²/R

R = ρL/A · ε = V + Ir · V_out = V_in × R₂/(R₁+R₂)

Series: R_T = R₁+R₂ · Parallel: 1/R_T = 1/R₁ + 1/R₂

Materials

ρ = m/V · p = F/A · p = hρg · F_upthrust = ρVg

F = kx · E_elastic = ½kx² = ½Fx

σ = F/A · ε = x/L₀ · E = σ/ε

F_drag = 6πηrv (Stokes' Law, laminar flow only)

Waves & Quantum

v = fλ · T = 1/f · I = P/A · n = c/v · n₁ sinθ₁ = n₂ sinθ₂

sin C = 1/n · d sinθ = nλ · w = λD/s

E = hf = hc/λ · hf = φ + ½mv²_max · φ = hf₀

λ = h/p = h/mv (de Broglie)

Constants

g = 9.81 m s⁻² · c = 3.00 × 10⁸ m s⁻¹ · h = 6.63 × 10⁻³⁴ J s

e = 1.60 × 10⁻¹⁹ C · m_e = 9.11 × 10⁻³¹ kg · m_p = 1.67 × 10⁻²⁷ kg

Calculation tips:

Show every step — method marks awarded even if final answer wrong

Always write the formula first, then substitute with units

Check units throughout; convert to SI before substituting (mm→m, g→kg)

Use scientific notation for very large/small answers (e.g. 3.2 × 10⁻¹⁹ J)

Round to 3 significant figures unless told otherwise

Explanation vocabulary (use these exact phrases):

"The resultant force is zero" (not "balanced forces")

"Rate of change of momentum" (not "change in momentum")

"Energy is transferred to the surroundings as thermal energy" (not "lost")

"The wavelength decreases" (not "the wave slows down")

"The frequency remains constant" when a wave changes medium

Practical answer structure (6-mark questions):

1. Identify independent, dependent, and all control variables

2. Name all apparatus + method to measure each quantity + suitable ranges

3. Repeat readings and calculate mean to reduce random error

4. Describe the graph to plot and what the gradient gives

5. State one safety precaution with a specific reason

6. State one improvement with a specific benefit (e.g. "use vernier caliper for ±0.1 mm")

Common mistakes to avoid:

Projectile: horizontal v = const; only vertical v changes — don't mix them up

Moments: always state the pivot; use perpendicular distance

Internal resistance: ε is the EMF, V is the terminal p.d. — they are not the same

Photoelectric: intensity only affects rate of emission, NOT KE of electrons

Snell's Law: always measure angles from the normal, not the surface

Young Modulus: use original length L₀, not deformed length

Graph-drawing rules:

Label both axes with quantity and unit (e.g. Force / N)

Use more than half the grid; scale in 1, 2, 5 or 10 multiples only

Draw smooth best-fit line (or curve) — do not just join dots

Gradient: draw largest possible triangle; show Δy and Δx clearly

If the line should pass through origin, check if it does (systematic error if not)