Engineering physics

What engineering physics covers

One of the five AQA option units, so check whether it is yours before revising it. It has two halves that meet at the end: rotational mechanics, which repeats Year 12 mechanics with angles in place of distances, and thermodynamics, which extends the work done by a gas into a treatment of engines. Mechanics and thermal physics are both assumed.

The main ideas

• Angular displacement, velocity and acceleration in radians, with four angular equations of motion used exactly as SUVAT is.
• Moment of inertia as a measure of how mass is distributed, and rotational kinetic energy, including a flywheel as an energy store.
• Torque linked to angular acceleration, angular momentum conserved without an external torque, and angular impulse.
• Work and power in rotation.
• The first law of thermodynamics with AQA's sign convention, and work read as the area under a p-V curve.
• The four non-flow processes, and which term, if any, each sets to zero.
• The engine cycle and its efficiency ceiling, four-stroke petrol and diesel engines, indicator diagrams, a power audit of a real engine, and refrigerators and heat pumps as engines run backwards.

Key equations

ω₂ = ω₁ + αt     θ = ω₁t + 12αt²$\omega_{2} = \omega_{1} + \alpha t \qquad \theta = \omega_{1}t + \tfrac{1}{2}\alpha t^{2}$ω_2 = ω_1 + αt θ = ω_1t + (1/2)αt^2

the angular equations, for constant angular acceleration

E_k = 12Iω²$E_{k} = \tfrac{1}{2}I\omega^{2}$E_k = (1/2)Iω^2

rotational kinetic energy

T = Iα      angular momentum = Iω$T = I\alpha \qquad \text{angular momentum} = I\omega$T = Iα angular momentum = Iω

torque, and the quantity conserved without an external torque

P = Tω$P = T\omega$P = Tω

power delivered by a torque

Q = ΔU + W$Q = \Delta U + W$Q = ΔU + W

the first law, with W the work done by the gas

efficiency = WQ_H      maximum = T_H - T_CT_H$\text{efficiency} = \frac{W}{Q_H} \qquad \text{maximum} = \frac{T_H - T_C}{T_H}$efficiency = (W/Q_H) maximum = (T_H - T_C)/T_H

a real engine against its ceiling, in kelvin

Every equation the engineering physics notes display is collected, with its conditions, on the engineering physics equations page.

Common errors

• Moment of inertia depends on where the mass sits, not only how much there is, so two objects of equal mass can be very different to set spinning.
• In AQA's statement of the first law, W is the work done by the gas, so a compression contributes a negative W. Reading the convention off the question prevents most sign errors here.
• The maximum theoretical efficiency uses absolute temperatures and is a ceiling no design can pass. A real engine reaching half of it is normal.
• When two rotating bodies couple together, angular momentum is conserved and kinetic energy is not, exactly as in a linear inelastic collision.

Suggested order

Rotational motion and moment of inertia first, then torque and angular momentum to finish the mechanical half. The first law of thermodynamics and non-flow processes next, since the heat engine lessons build on them. Leave heat engines and heat pumps until the rest is secure.