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Advanced Higher Physics relationships sheet: every relationship and what is not on it

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Formula sheet

The card below opens today's Advanced Higher Physics paper with the relationships sheet in the drawer. The contents follow in our own layout. The 2026 sheet was the same as the 2025 sheet. Check it against the 2026 sheet before you rely on this page.

Formula sheet

Advanced Higher Physics

Open formula sheet

Kinematics

v=\frac{ds}{dt}velocity
a=\frac{dv}{dt}=\frac{d^2s}{dt^2}acceleration
v=u+atfinal velocity
s=ut+\frac{1}{2}at^2displacement
v^2=u^2+2asvelocity from displacement

Rotational motion

\omega=\frac{d\theta}{dt}angular velocity
\alpha=\frac{d\omega}{dt}=\frac{d^2\theta}{dt^2}angular acceleration
\omega=\omega_0+\alpha tfinal angular velocity
\theta=\omega_0t+\frac{1}{2}\alpha t^2angular displacement
\omega^2=\omega_0^2+2\alpha\thetaangular velocity from angular displacement
s=r\thetaarc length
v=r\omegatangential speed
a_t=r\alphatangential acceleration
a_r=\frac{v^2}{r}=r\omega^2radial acceleration
F=\frac{mv^2}{r}=mr\omega^2centripetal force
L=mvr=mr^2\omegaangular momentum
L=I\omegaangular momentum from the moment of inertia
E_k=\frac{1}{2}I\omega^2rotational kinetic energy
\tau=Frtorque
\tau=I\alphatorque and angular acceleration
I=\sum mr^2moment of inertia of a set of masses
\omega=2\pi f=\frac{2\pi}{T}angular frequency

Gravitation and astrophysics

F=\frac{GMm}{r^2}gravitational force
V=-\frac{GM}{r}gravitational potential
E_P=Vm=-\frac{GMm}{r}gravitational potential energy
F=\frac{GMm}{r^2}=\frac{mv^2}{r}=mr\omega^2=mr\left(\frac{2\pi}{T}\right)^2orbiting body: gravity as the centripetal force
v_{esc}=\sqrt{\frac{2GM}{r}}escape speed
r_{Schwarzschild}=\frac{2GM}{c^2}Schwarzschild radius
L=4\pi r^2\sigma T^4luminosity of a star
\frac{P}{A}=\sigma T^4power per unit area from a black body
b=\frac{L}{4\pi d^2}apparent brightness
E_P=E_k(\text{translational})+E_k(\text{rotational})potential energy converted to translational and rotational kinetic energy

Quanta and particles

E=hfphoton energy
\lambda=\frac{h}{p}de Broglie wavelength
mvr=\frac{nh}{2\pi}Bohr quantisation
\Delta x\Delta p_x\geq\frac{h}{4\pi}uncertainty in position and momentum
\Delta E\Delta t\geq\frac{h}{4\pi}uncertainty in energy and time

Oscillations and waves

y=A\cos\omega t\ \text{or}\ y=A\sin\omega tdisplacement in simple harmonic motion
a=\frac{d^2y}{dt^2}=-\omega^2yacceleration in simple harmonic motion
F=-kyrestoring force of a spring
v=\pm\omega\sqrt{A^2-y^2}velocity in simple harmonic motion
E_k=\frac{1}{2}m\omega^2(A^2-y^2)kinetic energy in simple harmonic motion
E_P=\frac{1}{2}m\omega^2y^2potential energy in simple harmonic motion
E=\frac{1}{2}kA^2total energy of a spring system
y=A\sin2\pi\left(ft-\frac{x}{\lambda}\right)progressive wave
\varphi=\frac{2\pi x}{\lambda}phase difference
\Delta x=\frac{\lambda l}{2d}fringe spacing, wedge
d=\frac{\lambda}{4n}thin film thickness, a quarter of the wavelength in the film
\Delta x=\frac{\lambda D}{d}fringe spacing, double slit
\tan i_P=nBrewster angle
\text{opd}=n\times\text{gpd}optical path difference
\text{opd}=m\lambda\ \text{or}\ \left(m+\frac{1}{2}\right)\lambdapath difference for a maximum or minimum, m = 0, 1, 2 and so on

Electric and magnetic fields

F=\frac{Q_1Q_2}{4\pi\varepsilon_0r^2}force between point charges
E=\frac{Q}{4\pi\varepsilon_0r^2}electric field of a point charge
V=\frac{Q}{4\pi\varepsilon_0r}electric potential of a point charge
F=QEforce on a charge in an electric field
V=Eduniform field
W=QVwork done moving a charge
E_k=\frac{1}{2}mv^2kinetic energy
F=qvBforce on a charge moving in a magnetic field
F=IlB\sin\thetaforce on a conductor
B=\frac{\mu_0I}{2\pi r}magnetic field near a long wire
c=\frac{1}{\sqrt{\varepsilon_0\mu_0}}the speed of light

Circuits and electromagnetism

V_{rms}=\frac{V_{peak}}{\sqrt{2}}root mean square voltage
I_{rms}=\frac{I_{peak}}{\sqrt{2}}root mean square current
Q=Itcharge
V=IRvoltage
P=IV=I^2R=\frac{V^2}{R}power
R_T=R_1+R_2+\cdotsresistors in series
\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\cdotsresistors in parallel
E=V+Ire.m.f. and internal resistance
V_1=\frac{R_1}{R_1+R_2}V_svoltage across one resistor in a potential divider
\frac{V_1}{V_2}=\frac{R_1}{R_2}voltage ratio in a potential divider
C=\frac{Q}{V}capacitance
E=\frac{1}{2}QV=\frac{1}{2}CV^2=\frac{1}{2}\frac{Q^2}{C}energy stored in a capacitor
\tau=RCtime constant
X_C=\frac{V}{I}=\frac{1}{2\pi fC}reactance of a capacitor
X_L=\frac{V}{I}=2\pi fLreactance of an inductor
E=\frac{1}{2}LI^2energy stored in an inductor
\varepsilon=-L\frac{dI}{dt}induced e.m.f.

Uncertainties

\frac{\Delta W}{W}=\sqrt{\left(\frac{\Delta X}{X}\right)^2+\left(\frac{\Delta Y}{Y}\right)^2+\left(\frac{\Delta Z}{Z}\right)^2}relative uncertainty of a product or quotient
\Delta W=\sqrt{\Delta X^2+\Delta Y^2+\Delta Z^2}uncertainty of a sum or difference
\left(\frac{\Delta W^n}{W^n}\right)=n\left(\frac{\Delta W}{W}\right)uncertainty of a power

Higher Physics relationships

d=vtdistance = speed × time
s=vtdisplacement = velocity × time
s=\frac{1}{2}(u+v)tdisplacement from average velocity
W=mgweight
F=maforce
E_w=Fdwork done
E_p=mghgravitational potential energy
P=\frac{E}{t}power
p=mvmomentum
Ft=mv-muimpulse
F=\frac{Gm_1m_2}{r^2}gravitational force between two masses
t^{\prime}=\frac{t}{\sqrt{1-\left(\frac{v}{c}\right)^2}}time dilation
l^{\prime}=l\sqrt{1-\left(\frac{v}{c}\right)^2}length contraction
f_o=f_s\left(\frac{v}{v\pm v_s}\right)Doppler effect for a moving source
z=\frac{\lambda_{\text{observed}}-\lambda_{\text{rest}}}{\lambda_{\text{rest}}}redshift from wavelengths
z=\frac{v}{c}redshift from speed
v=H_0dHubble's law
E=mc^2mass-energy equivalence
E_k=hf-hf_0photoelectric effect
E_2-E_1=hfenergy level transition
T=\frac{1}{f}period
v=f\lambdawave speed
d\sin\theta=m\lambdagrating equation
n=\frac{\sin\theta_1}{\sin\theta_2}refractive index
\frac{\sin\theta_1}{\sin\theta_2}=\frac{\lambda_1}{\lambda_2}=\frac{v_1}{v_2}refraction in terms of wavelength and speed
\sin\theta_c=\frac{1}{n}critical angle
I=\frac{k}{d^2}intensity and distance
I=\frac{P}{A}intensity and power
I_1d_1^2=I_2d_2^2inverse square law between two points
\text{path difference}=m\lambda\ \text{or}\ \left(m+\frac{1}{2}\right)\lambdapath difference for a maximum or minimum, m = 0, 1, 2 and so on
\frac{\text{max value}-\text{min value}}{\text{number of values}}random uncertainty
\Delta R=\frac{R_{max}-R_{min}}{n}the same, for a quantity R

Additional relationships

C=2\pi rcircumference of a circle
A=\pi r^2area of a circle
A=4\pi r^2area of a sphere
V=\frac{4}{3}\pi r^3volume of a sphere
\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}sine
\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}cosine
\tan\theta=\frac{\text{opposite}}{\text{adjacent}}tangent
\sin^2\theta+\cos^2\theta=1the link between sine and cosine
I=mr^2moment of inertia of a point mass
I=\frac{1}{12}ml^2moment of inertia of a rod about its centre
I=\frac{1}{3}ml^2moment of inertia of a rod about its end
I=\frac{1}{2}mr^2moment of inertia of a disc about its centre
I=\frac{2}{5}mr^2moment of inertia of a sphere about its centre
\frac{d}{dx}(\sin ax)=a\cos axderivative of sin ax
\frac{d}{dx}(\cos ax)=-a\sin axderivative of cos ax
\int\sin ax\ dx=-\frac{1}{a}\cos ax+cintegral of sin ax
\int\cos ax\ dx=\frac{1}{a}\sin ax+cintegral of cos ax

The last page of the sheet lists the electron arrangements of the elements. The sheet is printed as one list, and the groups here are ours. The data sheet in the specimen paper is headed Common Physical Quantities, and the paper says candidates may refer to it and to the relationships sheet.

What is not on the Advanced Higher Physics relationships sheet

  • Constants. G, h, c, the mass and charge of the electron and the permittivity and permeability of free space are on the data sheet, not the relationships sheet.
  • Symbols and units. The sheet gives no names and no units.
  • Which one to use. A question on a satellite can use any of four forms of the centripetal force. Pick the form that has your known quantities.
  • Rearranging, and calculus. The sheet gives rates such as dv/dt, so you must know how to differentiate and integrate.
  • Descriptions. The physics of fields, interference and relativity needs words, and no words are given.

How the paper uses the sheets

The course specification gives the question paper 130 marks and 2 hours 30 minutes, and the project 30 marks. It says a data sheet and a relationships sheet are provided. In the 2027 timetable the exam is on Tuesday 4 May from 09:00 to 11:30 (Exam Timetable 2027, version 02). Our Advanced Higher Physics guide covers the course and the grades.

Using the sheets under exam pressure

Radial acceleration

A car takes a bend of radius 50 m at 15 m/s. The sheet gives a = v²/r, so a = 225 ÷ 50 = 4.5 m/s². Check it in the Circular Motion Calculator.

Moment of inertia and torque

A uniform disc of mass 2.0 kg and radius 0.30 m has a torque of 0.45 N m applied about its centre. The disc about its centre has I = ½mr², so

I=\frac{1}{2}\times2.0\times0.30^2=0.090\ \text{kg m}^2,\qquad\alpha=\frac{\tau}{I}=\frac{0.45}{0.090}=5.0\ \text{rad s}^{-2}

A relationship plus a constant from the data sheet

An electron moves at 2.0 × 10⁶ m/s. Find its de Broglie wavelength. The relationship is λ = h ÷ p with p = mv, and the specimen data sheet gives h = 6.63 × 10⁻³⁴ J s and the electron mass as 9.11 × 10⁻³¹ kg:

\lambda=\frac{h}{mv}=\frac{6.63\times10^{-34}}{9.11\times10^{-31}\times2.0\times10^{6}}=3.6\times10^{-10}\ \text{m}

Practise photon energy in the Light and Energy course, then press Mark.

Work out a photon energy from its frequency or wavelength, in units of 10^-19 J.

Press Mark to have your answer marked in the Light & Energy course.

Exam answers

The answers and a worked mark scheme come with today's paper once it is marked. Sit the paper with the sheet open beside you, mark it, and the worked answers show which line each question wanted. We do not publish official or past paper answers.

Use the sheet with today's paper

Uni-Sine publishes a free daily paper for Advanced Higher Physics. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full SQA paper and not set by SQA. Many schools set a longer prelim in winter: see our prelims guide. Open the sheet, set a timer, and write the line you use at the start of each answer.

Common mistakes

  • Mixing up the three rotational equations. They mirror v = u + at, s = ut + ½at² and v² = u² + 2as, with ω, θ and α in place.
  • Using degrees for angular quantities. Radians per second are the unit for ω.
  • Choosing the wrong moment of inertia. The rod about its end has ⅓ml², and about its centre ⅟₁₂ml².
  • Mixing up fringe spacing formulas. The wedge and the double slit have different results.
  • Adding uncertainties directly. The sheet combines them by adding squares and taking a square root.

Common questions

Do you get a relationships sheet in Advanced Higher Physics?
Yes. SQA provides a relationships sheet and a data sheet with the question paper.
What is on the Advanced Higher Physics relationships sheet?
Relationships for kinematics, rotation, gravitation, quanta, simple harmonic motion, waves, fields, circuits, inductors and uncertainties, the Higher Physics relationships repeated, plus moments of inertia and standard derivatives and integrals.
Are the constants on the relationships sheet?
No. Constants are on the data sheet, which is printed in the question paper.
Are the moments of inertia given?
Yes, for a point mass, a rod about its centre and end, a disc and a sphere.
Is the Advanced Higher Physics relationships sheet the same every year?
The 2026 sheet was the same as the 2025 sheet.

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Scotland · Advanced HigherAdvanced Higher Physics: 2027 Exam Guide and PracticeAdvanced Higher Physics explained: the shorter 2027 exam, the project, the relationships sheet, 2026 grade boundaries, the topics and worked questions.