Physics › Engineering physics

Engineering physics

The option unit for engines and machines: rotation reruns mechanics with angles in place of metres, and thermodynamics settles what any engine can and cannot do with the heat it is fed.

Year 13 · 4 topics · AQA option unit.

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 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.

The equations it turns on

$\omega_{2} = \omega_{1} + \alpha t \qquad \theta = \omega_{1}t + \tfrac{1}{2}\alpha t^{2}$: the angular equations, for constant angular acceleration
$E_{k} = \tfrac{1}{2}I\omega^{2}$: rotational kinetic energy
$T = I\alpha \qquad \text{angular momentum} = I\omega$: torque, and the quantity conserved without an external torque
$P = T\omega$: power delivered by a torque
$Q = \Delta U + W$: the first law, with W the work done by the gas
$\text{efficiency} = \frac{W}{Q_H} \qquad \text{maximum} = \frac{T_H - T_C}{T_H}$: a real engine against its ceiling, in kelvin

Where it usually goes wrong

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.

Where to start

Rotational motion and moment of inertia first, then torque and angular momentum to finish the mechanical half. The first law of thermodynamics next, since heat engines is written on top of it. Heat engines and heat pumps is the longest lesson and is best left until the rest is secure.