OCR A-level Physics A (H556) · Module 5: Newtonian World and Astrophysics
Mini-Lesson
Newtonian World & Astrophysics
Module 5 sweeps from molecules to galaxies: thermal physics, circular motion, oscillations, gravitational fields, and astrophysics and cosmology.
E = mcΔθ · pV = nRT = NkT · a = v²/r = ω²r · a = −ω²x · g = GM/r² · λmaxT = 2.898 × 10⁻³ m Kfive chapters, one Newtonian world view — right up to the point where it stops working
The unifying idea: Newton's laws plus an inverse-square force explain a molecule in a box, a satellite in orbit and a galaxy in a cluster. This module is Newtonian physics operating at every scale it can reach.
Work through each screen, answer the questions as you go (several are full A-level calculations) and collect ⭐ stars. Press Start when you're ready.
Module 5 · thermal physics
Internal energy, heat capacity and latent heat
Internal energy is the sum of the random kinetic and potential energies of all the molecules. Temperature is a measure of the mean kinetic energy only.
E = mcΔθ · E = mLc = specific heat capacity (J kg⁻¹ K⁻¹) · L = specific latent heat (J kg⁻¹)
During a change of state the temperature stays constant: the energy goes into breaking bonds, i.e. into the potential part of the internal energy.
Absolute zero (0 K = −273.15 °C) is the temperature of minimum internal energy. Always convert to kelvin for gas calculations.
For an ideal gas there are no intermolecular forces, so the internal energy is entirely kinetic and depends only on T.
Calculate
Your turn — specific heat capacity
1Calculate the energy needed to raise the temperature of 2.0 kg of aluminium by 30 K. (c = 900 J kg⁻¹ K⁻¹.) Give your answer in kJ.
kJ
Hint: E = mcΔθ = 2.0 × 900 × 30 = 54 000 J. Divide by 1000.
Module 5 · gases
The ideal gas equation and kinetic theory
pV = nRT = NkTR = 8.31 J mol⁻¹ K⁻¹ · k = 1.38 × 10⁻²³ J K⁻¹ · and k = R/N_A
Kinetic theory derives this from Newton's laws applied to molecules. The assumptions: molecules are point-like, in continuous random motion, exert no forces except during collisions, and all collisions are perfectly elastic.
pV = ⅓ N m ⟨c²⟩ → ½ m ⟨c²⟩ = (3/2) kTthe mean kinetic energy of a molecule is directly proportional to the ABSOLUTE temperature
The trap: doubling the absolute temperature doubles the mean KE — but the rms speed only rises by a factor of √2, because KE goes as the square of the speed.
Calculate
Your turn — counting molecules
2A gas at a pressure of 1.0 × 10⁵ Pa occupies 0.020 m³ at 293 K. Use pV = NkT to find the number of molecules N. Give your answer as a multiple of 10²³ to 3 significant figures. (k = 1.38 × 10⁻²³ J K⁻¹)
ω = 2π/T · v = rω · a = v²/r = ω²r · F = mv²/r = mω²rthe centripetal force always points to the CENTRE — and does no work
An object in circular motion at constant speed is still accelerating, because the direction of its velocity is constantly changing. The centripetal force is not a new force: it is whatever real force is doing the job (tension, friction, gravity).
SHM: a = − ω² x · x = A cos(ωt) · vmax = ωAmass–spring: T = 2π√(m/k) · simple pendulum: T = 2π√(l/g)
SHM is defined by a ∝ −x: acceleration proportional to displacement and always towards equilibrium.
The period is independent of amplitude.
Energy: total E = ½kA²; KE is maximum at equilibrium, PE at the extremes; the total is constant if undamped.
Damping reduces amplitude. Resonance occurs when the driving frequency equals the natural frequency — heavier damping lowers and broadens the peak.
Calculate
Your turn — angular velocity
3A satellite orbits the Earth with a period of 90 minutes. Calculate its angular velocity. Give your answer as a multiple of 10⁻³ rad s⁻¹ to 3 significant figures.
× 10⁻³ rad s⁻¹
Hint: T = 90 × 60 = 5400 s. ω = 2π/T = 2π ÷ 5400 = 1.164 × 10⁻³ rad s⁻¹.
Calculate
Your turn — pendulum length
4A simple pendulum has a period of exactly 2.0 s. Taking g = 9.81 m s⁻², calculate its length. Give your answer in m to 3 significant figures.
m
Hint: T = 2π√(l/g), so l = gT²/(4π²) = (9.81 × 4.0) ÷ 39.48.
Quick check
Does the centripetal force do work?
?A ball on a string is whirled in a horizontal circle at constant speed. How much work does the tension do on it?
Sort it
Which chapter of Module 5?
Tap an idea, then tap the chapter it belongs to.
🌡️ Thermal physics
🎡 Circular motion & SHM
🔭 Astrophysics
Module 5 · gravitational fields
Gravitational fields and orbits
F = GMm/r² · g = GM/r² · Vg = −GM/rG = 6.67 × 10⁻¹¹ N m² kg⁻² · gravitational potential is always NEGATIVE, and zero at infinity
For a satellite in a circular orbit, gravity provides the centripetal force:
GMm/r² = mv²/r → v = √(GM/r) → T² = (4π²/GM) r³Kepler's third law: T² ∝ r³ — and the satellite's own mass cancels out
A geostationary satellite has a 24-hour period, orbits west to east above the equator, and sits at r ≈ 4.22 × 10⁷ m.
Escape velocity: v = √(2GM/r) — the speed needed for the kinetic energy to equal the depth of the potential well.
Calculate
Your turn — g on Mars
5Mars has mass 6.42 × 10²³ kg and radius 3.39 × 10⁶ m. Calculate the gravitational field strength at its surface. (G = 6.67 × 10⁻¹¹ N m² kg⁻².) Give your answer in N kg⁻¹ to 3 significant figures.
A star is born when a cloud of gas and dust collapses under gravity until the core is hot enough to fuse hydrogen into helium. What follows depends on mass:
Low mass (Sun-like): main sequence → red giant → planetary nebula → white dwarf. The core is supported by electron degeneracy pressure, up to the Chandrasekhar limit of about 1.4 solar masses.
High mass: main sequence → red supergiant → supernova → neutron star or black hole.
λmax T = 2.898 × 10⁻³ m K · L = 4πr²σT⁴Wien's displacement law · Stefan's law, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
On the HR diagram, luminosity is plotted against temperature — with temperature increasing to the LEFT. The main sequence runs from hot, luminous stars at the top left to cool, dim ones at the bottom right.
z = Δλ/λ = v/c · v = H₀ dredshift and Hubble's law: the Universe is expanding, and age ≈ 1/H₀
Evidence for the Big Bang: the redshift–distance relation, the cosmic microwave background at 2.7 K, and the observed abundance of helium. Observations of distant type Ia supernovae show the expansion is accelerating — attributed to dark energy.
Calculate
Your turn — Wien's law
6The red supergiant Betelgeuse has a surface temperature of about 3600 K. Calculate the wavelength at which it emits most strongly. Give your answer in nm to 3 significant figures. (Wien constant = 2.898 × 10⁻³ m K)
nm
Hint: λ_max = 2.898 × 10⁻³ ÷ T = 2.898 × 10⁻³ ÷ 3600 = 8.05 × 10⁻⁷ m. Multiply by 10⁹ for nm.
Quick check
White dwarfs on the HR diagram
?Where do white dwarfs sit on a Hertzsprung–Russell diagram?
Quick check
Resonance
?A system is driven at increasing frequency. Its amplitude peaks sharply when the driving frequency equals its natural frequency. Adding damping will:
Match it
Match the quantity to its equation
Tap an item on the left, then its partner on the right.
Quantity
Equation
Recap
The big ideas to know
Thermal: E = mcΔθ (temperature changes) · E = mL (state changes) · absolute zero = 0 K = −273.15 °C