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Engineering physics equations

The 25 equations the engineering physics notes display, each with a link to the lesson that states it. Of the 25, the data booklet prints 24 and 1 is yours to memorise.

Year 13 · 8 lessons with equations.

The marks refer to the AQA 7408 data booklet. An equation it prints is marked as such, and one it leaves out is marked to learn. An equation with no mark has not been checked against that booklet, and some of these belong to the Edexcel, OCR or CIE specification rather than AQA’s, so check them against your own board’s data or formula booklet.

8 lessons

Rotational motion and the angular equations

a=αra = \alpha rNOT IN THE AQA DATA BOOKLET: LEARN IT
ω2=ω1+αt\omega_{2} = \omega_{1} + \alpha tIN THE AQA DATA BOOKLET
ω22=ω12+2αθ\omega_{2}^{2} = \omega_{1}^{2} + 2\alpha\thetaIN THE AQA DATA BOOKLET
θ=ω1t+αt22\theta = \omega_{1}t + \frac{\alpha t^{2}}{2}IN THE AQA DATA BOOKLET
θ=(ω1+ω2)t2\theta = \frac{(\omega_{1} + \omega_{2})t}{2}IN THE AQA DATA BOOKLET

Moment of inertia and rotational kinetic energy

I=m1r12+m2r22+…I = m_{1}r_{1}^{2} + m_{2}r_{2}^{2} + \ldotsIN THE AQA DATA BOOKLET
Ek=12Iω2E_{k} = \frac{1}{2}I\omega^{2}IN THE AQA DATA BOOKLET

Torque and angular acceleration

T=FrT = FrIN THE AQA DATA BOOKLET
T=IαT = I\alphaIN THE AQA DATA BOOKLET

Angular momentum and rotational power

angular momentum=Iω\text{angular momentum} = I\omegaIN THE AQA DATA BOOKLET
TΔt=Δ(Iω)T\Delta t = \Delta(I\omega)IN THE AQA DATA BOOKLET
W=TθW = T\thetaIN THE AQA DATA BOOKLET
P=TωP = T\omegaIN THE AQA DATA BOOKLET

The first law and its sign convention

Q=ΔU+WQ = \Delta U + WIN THE AQA DATA BOOKLET
W=pΔVW = p\Delta VIN THE AQA DATA BOOKLET

Constant pressure; W is the work done by the gas.

Non-flow processes and p-V diagrams

pV=constantpV = \text{constant}IN THE AQA DATA BOOKLET
pVγ=constantpV^{\gamma} = \text{constant}IN THE AQA DATA BOOKLET

Heat engines and their efficiency

efficiency=WQH=QH−QCQH\text{efficiency} = \frac{W}{Q_{H}} = \frac{Q_{H} − Q_{C}}{Q_{H}}IN THE AQA DATA BOOKLET
maximum theoretical efficiency=TH−TCTH\text{maximum theoretical efficiency} = \frac{T_{H} − T_{C}}{T_{H}}IN THE AQA DATA BOOKLET
input power=calorific value×fuel flow rate\text{input power} = \text{calorific value} \times \text{fuel flow rate}IN THE AQA DATA BOOKLET
indicated power=area of loop×cycles per second×cylinders\text{indicated power} = \text{area of loop} \times \text{cycles per second} \times \text{cylinders}IN THE AQA DATA BOOKLET
P=TωP = T\omegaIN THE AQA DATA BOOKLET
friction power=indicated power−brake power\text{friction power} = \text{indicated power} − \text{brake power}IN THE AQA DATA BOOKLET

Heat pumps and combined heat and power

COPref=QCW=QCQH−QCCOP_{ref} = \frac{Q_{C}}{W} = \frac{Q_{C}}{Q_{H} − Q_{C}}IN THE AQA DATA BOOKLET
COPhp=QHW=QHQH−QCCOP_{hp} = \frac{Q_{H}}{W} = \frac{Q_{H}}{Q_{H} − Q_{C}}IN THE AQA DATA BOOKLET

Every equation in the library is indexed by unit on the equation index, and the engineering physics notes are where these equations are derived and used. The one the booklet leaves out is on the equations to memorise, alongside the rest of the course.

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