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Grade 12 Physics

Grade 12 Physics on Temari has 28 revision cards, arranged by the chapters of the Ethiopian national curriculum. Every card says when the rule applies, what each symbol in it stands for, and the mistake students most often make with it. They are free to read and need no account.

28
Cards
5
Chapters
16
Formulas
10
Reference tables
Grade 12 Physics
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30 August 2026
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Across the whole subject

QuantityHow it is definedDimensionsSI unit
Areal×bl \times b[L2][\mathrm{L^{2}}]m2\mathrm{m^{2}}
Volumel×b×hl \times b \times h[L3][\mathrm{L^{3}}]m3\mathrm{m^{3}}
Densitym÷Vm \div V[ML3][\mathrm{M\,L^{-3}}]kgm3\mathrm{kg\,m^{-3}}
Velocitys÷ts \div t[LT1][\mathrm{L\,T^{-1}}]ms1\mathrm{m\,s^{-1}}
AccelerationΔv÷t\Delta v \div t[LT2][\mathrm{L\,T^{-2}}]ms2\mathrm{m\,s^{-2}}
Forcem×am \times a[MLT2][\mathrm{M\,L\,T^{-2}}]N\mathrm{N}
Momentumm×vm \times v[MLT1][\mathrm{M\,L\,T^{-1}}]kgms1\mathrm{kg\,m\,s^{-1}}
ImpulseF×tF \times t[MLT1][\mathrm{M\,L\,T^{-1}}]Ns\mathrm{N\,s}
Work and energyF×dF \times d[ML2T2][\mathrm{M\,L^{2}\,T^{-2}}]J\mathrm{J}
PowerW÷tW \div t[ML2T3][\mathrm{M\,L^{2}\,T^{-3}}]W\mathrm{W}
Pressure and stressF÷AF \div A[ML1T2][\mathrm{M\,L^{-1}\,T^{-2}}]Pa\mathrm{Pa}
Young's modulusσ÷ϵ\sigma \div \epsilon[ML1T2][\mathrm{M\,L^{-1}\,T^{-2}}]Pa\mathrm{Pa}
Surface tensionF÷lF \div l[MT2][\mathrm{M\,T^{-2}}]Nm1\mathrm{N\,m^{-1}}
Coefficient of viscosityF÷(A×Δv/Δx)F \div (A \times \Delta v / \Delta x)[ML1T1][\mathrm{M\,L^{-1}\,T^{-1}}]Pas\mathrm{Pa\,s}
Angular displacements÷rs \div r[M0L0T0][\mathrm{M^{0}L^{0}T^{0}}]rad\mathrm{rad}
Angular velocityθ÷t\theta \div t[T1][\mathrm{T^{-1}}]rads1\mathrm{rad\,s^{-1}}
Angular accelerationω÷t\omega \div t[T2][\mathrm{T^{-2}}]rads2\mathrm{rad\,s^{-2}}
TorqueF×rF \times r[ML2T2][\mathrm{M\,L^{2}\,T^{-2}}]Nm\mathrm{N\,m}
Moment of inertiam×r2m \times r^{2}[ML2][\mathrm{M\,L^{2}}]kgm2\mathrm{kg\,m^{2}}
Angular momentumI×ωI \times \omega[ML2T1][\mathrm{M\,L^{2}\,T^{-1}}]kgm2s1\mathrm{kg\,m^{2}\,s^{-1}}
Gravitational constantFr2÷m1m2Fr^{2} \div m_{1}m_{2}[M1L3T2][\mathrm{M^{-1}\,L^{3}\,T^{-2}}]Nm2kg2\mathrm{N\,m^{2}\,kg^{-2}}
Spring constantF÷xF \div x[MT2][\mathrm{M\,T^{-2}}]Nm1\mathrm{N\,m^{-1}}
StrainΔl÷l\Delta l \div l[M0L0T0][\mathrm{M^{0}L^{0}T^{0}}]none

When you use it

Use this table to check an equation before you trust it. Both sides of a correct physics equation always carry the same dimensions, so a mismatch tells you a mistake happened without you having to find it first.

Watch out

Equal dimensions do not make an equation correct. Dimensional analysis cannot see a missing half, a stray 2π or a wrong sign, because pure numbers have no dimensions at all. It rules equations out; it never rules them in.

QuantityHow it is definedDimensionsSI unit
Heat and internal energyF×dF \times d[ML2T2][\mathrm{M\,L^{2}\,T^{-2}}]J\mathrm{J}
Temperature[Θ][\Theta]K\mathrm{K}
Specific heat capacityQ÷(mΔT)Q \div (m\,\Delta T)[L2T2Θ1][\mathrm{L^{2}\,T^{-2}\,\Theta^{-1}}]Jkg1K1\mathrm{J\,kg^{-1}\,K^{-1}}
Latent heatQ÷mQ \div m[L2T2][\mathrm{L^{2}\,T^{-2}}]Jkg1\mathrm{J\,kg^{-1}}
Thermal conductivityQL÷(AΔTt)QL \div (A\,\Delta T\,t)[MLT3Θ1][\mathrm{M\,L\,T^{-3}\,\Theta^{-1}}]Wm1K1\mathrm{W\,m^{-1}\,K^{-1}}
EntropyQ÷TQ \div T[ML2T2Θ1][\mathrm{M\,L^{2}\,T^{-2}\,\Theta^{-1}}]JK1\mathrm{J\,K^{-1}}
Universal gas constantPV÷nTPV \div nT[ML2T2Θ1N1][\mathrm{M\,L^{2}\,T^{-2}\,\Theta^{-1}\,N^{-1}}]Jmol1K1\mathrm{J\,mol^{-1}\,K^{-1}}
Boltzmann constantR÷NAR \div N_{A}[ML2T2Θ1][\mathrm{M\,L^{2}\,T^{-2}\,\Theta^{-1}}]JK1\mathrm{J\,K^{-1}}
Coefficient of linear expansionΔL÷(LΔT)\Delta L \div (L\,\Delta T)[Θ1][\Theta^{-1}]K1\mathrm{K^{-1}}

When you use it

Reach for this whenever temperature appears in a formula. Θ is a base dimension of its own, and forgetting it is the most common way a thermal calculation goes wrong on paper after looking right in your head.

Watch out

Specific heat capacity carries no mass dimension, but heat capacity does. One is per kilogram and the other is for the whole object, so swapping them silently changes an answer by a factor of the mass.

QuantityHow it is definedDimensionsSI unit
Electric current[I][\mathrm{I}]A\mathrm{A}
Electric chargeI×tI \times t[IT][\mathrm{I\,T}]C\mathrm{C}
Potential differenceW÷qW \div q[ML2T3I1][\mathrm{M\,L^{2}\,T^{-3}\,I^{-1}}]V\mathrm{V}
ResistanceV÷IV \div I[ML2T3I2][\mathrm{M\,L^{2}\,T^{-3}\,I^{-2}}]Ω\Omega
ResistivityRA÷lRA \div l[ML3T3I2][\mathrm{M\,L^{3}\,T^{-3}\,I^{-2}}]Ωm\Omega\,\mathrm{m}
Conductance1÷R1 \div R[M1L2T3I2][\mathrm{M^{-1}\,L^{-2}\,T^{3}\,I^{2}}]S\mathrm{S}
Capacitanceq÷Vq \div V[M1L2T4I2][\mathrm{M^{-1}\,L^{-2}\,T^{4}\,I^{2}}]F\mathrm{F}
Electric fieldF÷qF \div q[MLT3I1][\mathrm{M\,L\,T^{-3}\,I^{-1}}]NC1\mathrm{N\,C^{-1}}
Permittivity of free spaceq2÷(4πFr2)q^{2} \div (4\pi F r^{2})[M1L3T4I2][\mathrm{M^{-1}\,L^{-3}\,T^{4}\,I^{2}}]Fm1\mathrm{F\,m^{-1}}
Magnetic fluxV×tV \times t[ML2T2I1][\mathrm{M\,L^{2}\,T^{-2}\,I^{-1}}]Wb\mathrm{Wb}
Magnetic flux densityΦ÷A\Phi \div A[MT2I1][\mathrm{M\,T^{-2}\,I^{-1}}]T\mathrm{T}
InductanceΦ÷I\Phi \div I[ML2T2I2][\mathrm{M\,L^{2}\,T^{-2}\,I^{-2}}]H\mathrm{H}
Permeability of free space2πrB÷I2\pi r B \div I[MLT2I2][\mathrm{M\,L\,T^{-2}\,I^{-2}}]Hm1\mathrm{H\,m^{-1}}

When you use it

Every electrical dimension on this list is built from current, because current is the base quantity and charge is not. Derive charge as current × time first, and the rest of the column follows without memorising anything.

Watch out

Resistance and resistivity differ by one power of length, and that is the direction students reverse most. Resistivity is a property of the material and never changes with the shape of the wire; resistance is a property of that particular wire.

QuantityHow it is definedDimensionsSI unit
Frequency1÷T1 \div T[T1][\mathrm{T^{-1}}]Hz\mathrm{Hz}
Wavelength[L][\mathrm{L}]m\mathrm{m}
Wave number1÷λ1 \div \lambda[L1][\mathrm{L^{-1}}]m1\mathrm{m^{-1}}
IntensityP÷AP \div A[MT3][\mathrm{M\,T^{-3}}]Wm2\mathrm{W\,m^{-2}}
Planck's constantE÷fE \div f[ML2T1][\mathrm{M\,L^{2}\,T^{-1}}]Js\mathrm{J\,s}
Work functionhf0h f_{0}[ML2T2][\mathrm{M\,L^{2}\,T^{-2}}]J\mathrm{J}
Decay constant1÷t1 \div t[T1][\mathrm{T^{-1}}]s1\mathrm{s^{-1}}

When you use it

This is the shortest of the four cards and the one entrance-exam questions reach for most, because Planck's constant and angular momentum share the dimensions of [ML2T1][\mathrm{M\,L^{2}\,T^{-1}}] and examiners like asking why.

Watch out

Frequency and angular velocity both come out as [T1][\mathrm{T^{-1}}], and so does the decay constant. Dimensions cannot tell those three apart, which is a useful reminder of what the method is actually for.

01

Unit 1

bLd2b \propto \frac{L}{d^2}
bb
Apparent brightnessWm2W\,m^{-2}
LL
True brightness or luminosityWW
dd
Distance to astronomical objectmm

When you use it

Use this to relate the apparent brightness of an astronomical body to its luminosity and distance.

Watch out

Apparent brightness decreases with the square of distance, not linearly.

Drafted from Grade 12 Physics, pages 2-24, then checked twice before it went up

Missile TypePropulsionTrajectoryGoverning Physics
Cruise missileJet-propelled throughout flightControlled pathConservation of momentum
Ballistic missileRocket-powered in initial phase onlyArc trajectoryNewtonian mechanics and gravity

When you use it

Use this to contrast the flight phases, engines, and trajectories of cruise versus ballistic missiles.

Watch out

Ballistic missiles carry rocket engines that fire only in the initial launch phase, not throughout the flight.

Drafted from Grade 12 Physics, pages 2-24, then checked twice before it went up

R=ct2R = \frac{c t}{2}
RR
Distance to targetmm
cc
Speed of lightms1m\,s^{-1}
tt
Round trip travel timess

When you use it

Use this to calculate the distance between a radar station and a target from the time taken for the radio pulse to go and return.

Watch out

Always divide the total travel time by 2. The measured time covers the distance to the target and back.

Drafted from Grade 12 Physics, pages 2-24, then checked twice before it went up

TermImage AppearanceEcho PropertyBody Feature
AnechoicBlackNo sound reflectedFluid-filled regions
HypoechoicDark grayFewer sound reflectionsSoft body tissues
HyperechoicLight grayMany sound reflectionsDense structures

When you use it

Use this to identify and classify the different shade regions on a medical ultrasound monitor.

Watch out

Anechoic regions appear black because fluids reflect zero echo, not because sound is blocked.

Drafted from Grade 12 Physics, pages 2-24, then checked twice before it went up

02

Unit 2

T2r3=4π2GM\frac{T^2}{r^3} = \frac{4\pi^2}{G M}
TT
orbital periodss
rr
orbital radiusmm
GG
universal gravitational constantNm2kg2N\,m^2\,kg^{-2}
MM
mass of central bodykgkg

When you use it

Use when relating the orbital period of a planet or satellite to its average orbital radius around a central mass.

Watch out

The mass M in the denominator is the mass of the central body being orbited, not the orbiting satellite.

Drafted from Grade 12 Physics, pages 25-68, then checked twice before it went up

Fg=Gm1m2r2F_g = \frac{G m_1 m_2}{r^2}
FgF_g
gravitational forceNN
GG
universal gravitational constantNm2kg2N\,m^2\,kg^{-2}
m1m_1
mass of first objectkgkg
m2m_2
mass of second objectkgkg
rr
distance between centers of massmm

When you use it

Use to compute the gravitational attraction force acting between any two bodies with mass.

Watch out

The separation distance r is measured between the centers of the bodies, not between their surfaces.

Drafted from Grade 12 Physics, pages 25-68, then checked twice before it went up

R=v02sin2θgR = \frac{v_0^2 \sin 2\theta}{g}
RR
horizontal rangemm
v0v_0
initial velocityms1m\,s^{-1}
θ\theta
launch angleradrad
gg
acceleration due to gravityms2m\,s^{-2}

When you use it

Use when finding the horizontal range of a projectile launched from and landing on the same level ground.

Watch out

This equation applies only when the launch elevation and landing elevation are identical.

Drafted from Grade 12 Physics, pages 25-68, then checked twice before it went up

Linear motionRotational motion
vf=v0+atv_f = v_0 + a tωf=ω0+αt\omega_f = \omega_0 + \alpha t
Δs=v0t+12at2\Delta s = v_0 t + \frac{1}{2} a t^2Δθ=ω0t+12αt2\Delta\theta = \omega_0 t + \frac{1}{2}\alpha t^2
vf2=v02+2aΔsv_f^2 = v_0^2 + 2 a \Delta sωf2=ω02+2αΔθ\omega_f^2 = \omega_0^2 + 2\alpha \Delta\theta
Δs=v0+vf2t\Delta s = \frac{v_0 + v_f}{2} tΔθ=ω0+ωf2t\Delta\theta = \frac{\omega_0 + \omega_f}{2} t

When you use it

Use to solve rotational motion problems with constant angular acceleration by mapping directly from linear kinematics.

Watch out

All angular displacements must be converted to radians before substituting into these kinematic equations.

Drafted from Grade 12 Physics, pages 25-68, then checked twice before it went up

τ=Iα\tau = I \alpha
τ\tau
net torqueNmN\,m
II
moment of inertiakgm2kg\,m^2
α\alpha
angular accelerationrads2rad\,s^{-2}

When you use it

Use to connect the net rotational force with rotational inertia and angular acceleration of a rigid body.

Watch out

Angular acceleration must always be in radians per second squared, never revolutions per second squared.

Drafted from Grade 12 Physics, pages 25-68, then checked twice before it went up

03

Fluid Mechanics

Pabs=Patm+PgageP_{\text{abs}} = P_{\text{atm}} + P_{\text{gage}}
PabsP_{\text{abs}}
absolute pressurePaPa
PatmP_{\text{atm}}
local atmospheric pressurePaPa
PgageP_{\text{gage}}
gauge pressurePaPa

When you use it

Use to convert between pressure gauge readings and the true absolute pressure relative to complete vacuum.

Watch out

Pressure measuring gauges read zero at atmospheric pressure. Never substitute gauge pressure directly into the ideal gas equation without adding atmospheric pressure.

Drafted from Grade 12 Physics, pages 69-117, then checked twice before it went up

FB=ρfluidgVdispF_B = \rho_{\text{fluid}} g V_{\text{disp}}
FBF_B
buoyant forceNN
ρfluid\rho_{\text{fluid}}
density of the surrounding fluidkgm3kg\,m^{-3}
gg
acceleration due to gravityms2m\,s^{-2}
VdispV_{\text{disp}}
volume of fluid displacedm3m^3

When you use it

Use to determine the upward buoyant force acting on any partially or completely submerged object in a fluid.

Watch out

Use the density of the fluid, not the density of the object, to calculate the buoyant force.

Drafted from Grade 12 Physics, pages 69-117, then checked twice before it went up

VdispVobj=ρobjρfluid\frac{V_{\text{disp}}}{V_{\text{obj}}} = \frac{\rho_{\text{obj}}}{\rho_{\text{fluid}}}
VdispV_{\text{disp}}
volume submerged in fluidm3m^3
VobjV_{\text{obj}}
total volume of the objectm3m^3
ρobj\rho_{\text{obj}}
density of the floating objectkgm3kg\,m^{-3}
ρfluid\rho_{\text{fluid}}
density of the fluidkgm3kg\,m^{-3}

When you use it

Use to calculate the fraction or percentage of a floating object submerged beneath the surface of a fluid.

Watch out

This equation applies only to floating objects in static equilibrium, where the object density is less than the fluid density.

Drafted from Grade 12 Physics, pages 69-117, then checked twice before it went up

F1A1=F2A2\frac{F_1}{A_1} = \frac{F_2}{A_2}
F1F_1
force applied on input pistonNN
A1A_1
cross-sectional area of input pistonm2m^2
F2F_2
force exerted on output pistonNN
A2A_2
cross-sectional area of output pistonm2m^2

When you use it

Use when finding the force or piston area in hydraulic lifts, brakes, and presses where confined fluid transmits pressure equally.

Watch out

Make sure the areas A_1 and A_2 are in the same units before calculating. If diameters are given, use area proportional to diameter squared.

Drafted from Grade 12 Physics, pages 69-117, then checked twice before it went up

P=P0+ρghP = P_0 + \rho g h
PP
absolute pressure at depth hPaPa
P0P_0
pressure at the fluid surfacePaPa
ρ\rho
density of the fluidkgm3kg\,m^{-3}
gg
acceleration due to gravityms2m\,s^{-2}
hh
depth below the surfacemm

When you use it

Use to calculate total hydrostatic pressure at any depth below the open surface of a static liquid.

Watch out

Always add atmospheric pressure P_0 when asked for absolute pressure. If only gauge pressure is required, omit P_0.

Drafted from Grade 12 Physics, pages 69-117, then checked twice before it went up

04

Electromagnetism

ε=NΔΦBΔt\varepsilon = -N \frac{\Delta\Phi_B}{\Delta t}
ε\varepsilon
induced electromotive forceV\text{V}
NN
number of turns in coil11
ΔΦB\Delta\Phi_B
change in magnetic fluxWb\text{Wb}
Δt\Delta t
change in times\text{s}

When you use it

Use to calculate the electromotive force induced in a coil by a changing magnetic flux.

Watch out

The negative sign represents Lenz law, indicating that the induced emf opposes the change in flux.

Drafted from Grade 12 Physics, pages 118-142, then checked twice before it went up

B=μ0I2πrB = \frac{\mu_0 I}{2\pi r}
BB
magnetic fieldT\text{T}
μ0\mu_0
permeability of free spaceTmA1\text{T}\cdot\text{m}\cdot\text{A}^{-1}
II
currentA\text{A}
rr
distance from the wirem\text{m}

When you use it

Use to calculate the magnetic field strength at a given distance from a long straight current-carrying wire.

Watch out

The distance r must be in meters, not centimeters or millimeters.

Drafted from Grade 12 Physics, pages 118-142, then checked twice before it went up

ΦB=BAcosθ\Phi_B = B A \cos\theta
ΦB\Phi_B
magnetic fluxWb\text{Wb}
BB
magnetic fieldT\text{T}
AA
aream2\text{m}^2
θ\theta
angle between magnetic field and normal to the areadegrees\text{degrees}

When you use it

Use to determine the total magnetic flux passing through a surface placed in a magnetic field.

Watch out

The angle theta is between the magnetic field and the area normal vector, not the surface plane.

Drafted from Grade 12 Physics, pages 118-142, then checked twice before it went up

When you use it

Use when given the angle between the magnetic field and the surface of a loop rather than its normal line.

Watch out

If the problem gives an angle with the surface plane, you must use 90 minus that angle for theta in the flux equation.

Drafted from Grade 12 Physics, pages 118-142, then checked twice before it went up

NpNs=VpVs\frac{N_p}{N_s} = \frac{V_p}{V_s}
NpN_p
primary coil turns11
NsN_s
secondary coil turns11
VpV_p
primary voltageV\text{V}
VsV_s
secondary voltageV\text{V}

When you use it

Use to relate primary and secondary voltages with the number of turns in an alternating current transformer.

Watch out

Transformers operate only with alternating current and cannot step up or step down direct current.

Drafted from Grade 12 Physics, pages 118-142, then checked twice before it went up

05

Basics of electronics

TypeDopant groupDopant examplesMajority carrierMinority carrier
N-typeGroup V (pentavalent)As, P, Sb, BiElectronsHoles
P-typeGroup III (trivalent)B, Al, Ga, InHolesElectrons

When you use it

Use to distinguish between N-type and P-type semiconductors, their impurities, and their charge carriers.

Watch out

Doped semiconductors remain electrically neutral overall even though one carrier type outnumbers the other.

Drafted from Grade 12 Physics, page 143 onwards, then checked twice before it went up

GateLogic operationOutput is 1 whenUniversal gate
ORAddition: y=A+By = A + BAt least one input is 1No
ANDMultiplication: y=ABy = A \cdot BAll inputs are 1No
NOTInversion: single inputInput is 0No
NORInverted ORAll inputs are 0Yes
NANDInverted ANDAt least one input is 0Yes

When you use it

Use to evaluate Boolean logic operations and outputs for digital logic circuits.

Watch out

In Boolean logic addition, 1 + 1 equals 1, representing TRUE OR TRUE, not arithmetic 2.

Drafted from Grade 12 Physics, page 143 onwards, then checked twice before it went up

When you use it

Use when determining the bias voltage polarities required across the junctions of a bipolar transistor for proper amplifier operation.

Watch out

The emitter-base junction must be forward biased and the collector-base junction must be reverse biased. Setting both junctions to forward bias is incorrect.

Drafted from Grade 12 Physics, page 143 onwards, then checked twice before it went up

β=ICIB,IE=IB+IC\beta = \frac{I_C}{I_B},\quad I_E = I_B + I_C
β\beta
Current gaindimensionlessdimensionless
ICI_C
Collector currentAA
IBI_B
Base currentAA
IEI_E
Emitter currentAA

When you use it

Use when calculating terminal currents or common-emitter current amplification in a bipolar junction transistor.

Watch out

Base current is given in microamperes while collector and emitter currents are in milliamperes. Convert all currents to amperes before computing.

Drafted from Grade 12 Physics, page 143 onwards, then checked twice before it went up

RegionDoping levelPhysical sizeFunction
EmitterHeavily dopedMedium sizeSupplies charge carriers
BaseLightly dopedVery thinPasses carriers to collector
CollectorModerately dopedLargest sizeCollects charge carriers

When you use it

Use to compare the doping levels, physical dimensions, and functions of the three regions of a bipolar junction transistor.

Watch out

The base is both the thinnest and the most lightly doped layer, while the collector is the largest in physical size.

Drafted from Grade 12 Physics, page 143 onwards, then checked twice before it went up

The papers these formulas are for

Real national exam questions from past years, with a worked answer for each one.

Open the past papers

The same subject in other years

An exam paper keeps asking for what the year below taught. Those cards are here too.

Questions students ask

What do the Grade 12 Physics cards cover?
28 cards across 5 chapters of the national textbook: Fluid Mechanics, Electromagnetism, Basics of electronics and 2 more. You can take any chapter one card at a time on the page itself.
Do these help with the Grade 12 national exam?
Yes. Grade 12 sits a national exam, and these are the Physics rules and formulas it expects you to know. Past papers with a worked answer behind every question are on the same site, also free.
Where do these cards come from?
They are drafted from Grade 12 Physics, the Ministry of Education textbook for this grade. A second pass that cannot see the chapter then re-derives every formula, constant and table row, and anything it cannot confirm is held back instead of published.
Is this free?
Yes. Every card here is free to read and the printable sheet is free to download. Neither needs an account.
When was this last checked?
30 August 2026. Cards arrive chapter by chapter, and the line under each one says when that card was last read through.

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