First SUVAT Equation
Formula: v = u + at
Final velocity equals initial velocity plus the product of uniform acceleration and time. Derived directly from the definition of acceleration.
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Every formula in the OCR A A-Level Physics specification (H556), with explanations. Built by Praneel Agrawal at Praneel Physics.
Formula: v = u + at
Final velocity equals initial velocity plus the product of uniform acceleration and time. Derived directly from the definition of acceleration.
Formula: s = ut + ½at²
Displacement equals initial velocity times time plus half the acceleration times time squared. Represents the area under a velocity-time graph.
Formula: v² = u² + 2as
Links final velocity, initial velocity, acceleration and displacement without requiring time. Derived by eliminating t from the first two SUVAT equations.
Formula: F = ma
The resultant force on an object equals its mass multiplied by its acceleration. The foundation of classical mechanics — acceleration is proportional to force and inversely proportional to mass.
Formula: p = mv
Momentum is the product of mass and velocity. A vector quantity — momentum is conserved in all closed systems (no external forces).
Formula: FΔt = Δ(mv)
Impulse (force multiplied by time) equals the change in momentum. The area under a force-time graph equals the impulse delivered.
Formula: Ek = ½mv²
Kinetic energy is proportional to mass and to the square of speed. Doubling speed quadruples kinetic energy. Derived from the work-energy theorem.
Formula: W = Fs cosθ
Work done equals force times displacement times the cosine of the angle between them. Only the component of force parallel to displacement does work.
Formula: P = W/t = Fv
Power is the rate of energy transfer. The form P = Fv is useful when force and velocity are both known.
Formula: v = rω
Linear (tangential) speed equals radius times angular velocity. Larger radius means faster linear speed at the same angular velocity — why the outer lane of a track is harder.
Formula: a = v²/r = rω²
Even at constant speed, circular motion requires inward acceleration because velocity direction is constantly changing. Always directed toward the centre.
Formula: F = mv²/r = mrω²
The net inward force required to maintain circular motion. Not a new type of force — it is provided by tension, gravity, friction, or magnetic force depending on the scenario.
Formula: F = GMm/r²
Every pair of masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of their separation. An inverse-square law.
Formula: g = GM/r²
Gravitational field strength is the force per unit mass at a point in the field. On Earth's surface g ≈ 9.81 N kg⁻¹, decreasing as 1/r² with altitude.
Formula: T² = (4π²/GM)r³
The square of orbital period is proportional to the cube of orbital radius. Derived by equating gravitational force to centripetal force and substituting v = 2πr/T.
Formula: x = A cos(ωt)
Displacement in simple harmonic motion varies sinusoidally with time. Amplitude A is the maximum displacement; ω = 2πf is angular frequency.
Formula: v = ±ω√(A² - x²)
Speed is maximum at equilibrium (x=0) and zero at the extremes (x=±A). Derived from energy conservation in SHM.
Formula: T = 2π√(m/k)
Period increases with mass and decreases with spring stiffness. Crucially independent of amplitude — the system is isochronous.
Formula: T = 2π√(l/g)
Period increases with pendulum length and decreases with gravitational field strength. Valid only for small angles (< 10°). Used to measure g experimentally.
Formula: F = kx
Force is proportional to extension within the elastic limit. The spring constant k is the gradient of the F-x graph. Beyond the elastic limit, permanent deformation occurs.
Formula: σ = F/A
Stress is force per unit cross-sectional area. Determines whether a material will fail — a thin wire under the same force as a thick one experiences higher stress.
Formula: ε = ΔL/L
Strain is fractional change in length — dimensionless. Normalises extension for samples of different original lengths.
Formula: E = σ/ε = FL/(AΔL)
Young's modulus is the gradient of the stress-strain graph in the elastic region. A material constant independent of sample size. Steel ≈ 200 GPa; rubber ≈ 0.05 GPa.
Formula: v = fλ
Wave speed equals frequency times wavelength. Wave speed depends on the medium; frequency is set by the source. Higher frequency means shorter wavelength at constant speed.
Formula: n₁ sinθ₁ = n₂ sinθ₂
Light bends toward the normal when entering a denser medium. The product n sinθ is conserved at any boundary. Total internal reflection occurs when θ exceeds the critical angle.
Formula: d sinθ = nλ
Constructive interference maxima occur when path difference between adjacent slits equals a whole number of wavelengths. Used to measure wavelengths of light precisely.
Formula: E = hf = hc/λ
Energy of a photon is proportional to frequency. Higher frequency (shorter wavelength) photons carry more energy. This explains the photoelectric effect.
Formula: hf = φ + ½mv²max
Photon energy is used to overcome the work function (escape energy) and any remainder becomes kinetic energy of the emitted electron. Threshold frequency f₀ = φ/h.
Formula: λ = h/p
All moving particles have an associated wavelength. Faster or heavier particles have shorter wavelengths. Explains electron diffraction and quantisation in atoms.
Formula: I = Q/t
Current is the rate of flow of charge. One ampere means one coulomb of charge flows per second. Conventional current flows from positive to negative.
Formula: V = IR
Potential difference equals current times resistance for ohmic conductors at constant temperature. Resistance R = V/I in all cases, even non-ohmic components.
Formula: P = VI = I²R = V²/R
All three forms are equivalent. P = I²R shows why doubling current quadruples power — critical for understanding fuse ratings and cable sizing.
Formula: R = ρL/A
Resistance is proportional to length and inversely proportional to cross-sectional area. Resistivity ρ is a material constant, independent of sample dimensions.
Formula: ε = I(R + r)
EMF drives current through both the external circuit (IR) and the battery itself (Ir — lost volts). Terminal voltage V = ε − Ir drops under load.
Formula: Q = CV
Charge stored is proportional to voltage for a given capacitor. Capacitance is defined as charge per unit voltage. 1 farad = 1 coulomb per volt.
Formula: E = ½CV² = ½QV = Q²/2C
Energy stored in the electric field between the plates. Factor of ½ arises because voltage builds gradually as charge accumulates.
Formula: Q = Q₀ e^(−t/RC)
Charge decays exponentially. The time constant τ = RC is the time for charge to fall to 37% of its initial value. After 5τ, discharge is 99% complete.
Formula: F = BIL sinθ
A current-carrying conductor in a magnetic field experiences a force. Maximum when current is perpendicular to field. Direction given by Fleming's Left-Hand Rule.
Formula: F = BQv sinθ
A charged particle moving across a magnetic field experiences a force perpendicular to its velocity — causing circular motion. Basis of mass spectrometers and particle accelerators.
Formula: Φ = BA cosθ
Magnetic flux measures the total field passing through a surface. Changing flux induces an EMF (Faraday's Law). A rotating coil has continuously changing flux — the basis of AC generators.
Formula: ε = −N dΦ/dt
The induced EMF is proportional to the rate of change of magnetic flux linkage. The minus sign (Lenz's Law) means the induced current opposes the change that causes it.
Formula: pV = nRT
Combines Boyle's Law, Charles's Law and Gay-Lussac's Law into one equation. Valid for ideal gases — point particles with elastic collisions and no intermolecular forces.
Formula: ½m⟨c²⟩ = 3kT/2
Temperature is a measure of mean molecular kinetic energy. Higher temperature means faster molecules. At absolute zero, molecular kinetic energy approaches zero.
Formula: N = N₀ e^(−λt)
The number of undecayed nuclei decreases exponentially. Radioactive decay is random and spontaneous at the individual nucleus level but statistically predictable for large samples.
Formula: t½ = ln2/λ
Half-life is the time for half the nuclei to decay — constant and independent of the amount present. Derived by setting N = N₀/2 in the decay law.
Formula: A = λN
Activity is the number of decays per second (measured in becquerels). Decreases exponentially following A = A₀ e^(−λt) — the same law as the number of nuclei.
Formula: E = mc²
Mass and energy are equivalent. In nuclear reactions the mass defect (difference in mass between reactants and products) corresponds to energy released as kinetic energy or gamma radiation.
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