Flywheel Applications Revision Notes | A Level AQA Physics

1. Why Flywheels Exist: The Problem They Solve

Picture the crankshaft of a car engine. The pistons fire in short, sharp bursts — each combustion stroke delivers a pulse of torque, then nothing until the next stroke. Without intervention, the shaft would lurch and slow between each pulse, making the engine rough and inefficient. The flywheel is the engineering solution to exactly this problem.

A flywheel is a disc or wheel with a deliberately large moment of inertia, mounted on the rotating shaft of a machine. Because it resists changes in angular velocity, it absorbs energy during the power stroke and releases it during the gaps, keeping the shaft spinning at a nearly constant rate. The result is smooth, continuous rotation from an inherently intermittent energy source.

This smoothing function is the core reason flywheels appear across engineering: from internal combustion engines and steam engines to industrial presses, pottery wheels, and modern energy-recovery systems. Understanding flywheels means understanding how rotational inertia can be put to practical work.

2. The Physics Behind the Flywheel

Recall from rotational dynamics that the moment of inertia $I$ plays the same role in rotation as mass does in linear motion. A large $I$ means the object strongly resists any change in its angular velocity $\omega$ — it takes a large net torque to speed it up or slow it down. This is precisely the property a flywheel exploits.

The key design insight is that mass concentrated at the rim contributes far more to $I$ than mass near the centre, because $I$ depends on $r^2$. Doubling the radius of a mass element quadruples its contribution to the moment of inertia. This is why many flywheels are built as heavy rings or have thick outer rims — the geometry maximises $I$ for a given total mass.

Notice the parallel with linear kinetic energy $E_k = \frac{1}{2}mv^2$: mass $m$ maps to moment of inertia $I$, and linear speed $v$ maps to angular velocity $\omega$. If you already have that linear equation secure, the rotational version follows the same structure. The difference is that $I$ encodes both how much mass there is and where it sits relative to the axis.

3. How a Flywheel Smooths Rotational Motion

Consider a single-cylinder engine. The combustion stroke delivers a large torque for a fraction of a revolution; the remaining three strokes (in a four-stroke cycle) contribute little or no driving torque. Without a flywheel, the angular velocity would rise sharply during the power stroke and fall between strokes — the shaft would oscillate in speed with every cycle.

With a flywheel attached, the large $I$ means the shaft's angular velocity changes only slightly in response to these torque fluctuations. During the power stroke, the excess torque (beyond what the load requires) accelerates the flywheel, storing energy. During the non-power strokes, the flywheel decelerates slightly, releasing that stored energy to maintain the load. The angular velocity stays nearly constant throughout.

The same principle applies in industrial machinery. A punch press, for example, requires a large torque for a brief instant when the punch meets the workpiece, but very little torque between punches. A flywheel stores energy from the motor during the idle phase and releases it during the punch, allowing a smaller, less powerful motor to drive the press effectively.

4. Calculating Energy Stored and Released

In exam questions, you will often need to find the energy a flywheel stores between two angular velocities, or the energy it can deliver as it slows from one speed to another. The key is that the energy exchanged equals the change in rotational kinetic energy.

Worked example: Calculating energy released by a flywheel as it slows

A flywheel has a moment of inertia of 4.0 kg m². During a power cut in a factory, the flywheel slows from 120 rad s⁻¹ to 80 rad s⁻¹ as it drives the machinery. Calculate the energy released by the flywheel. [3 marks]

1. $\Delta E_k = \frac{1}{2}I(\omega_1^2 - \omega_2^2)$ — The flywheel slows, so it releases energy. We take initial minus final to get a positive value for energy released. [M1 — correct equation]
2. $\omega_1^2 = 120 \times 120 = 14400 \text{ rad}^2\text{ s}^{-2}$ $\omega_2^2 = 80 \times 80 = 6400 \text{ rad}^2\text{ s}^{-2}$ — Always expand squares longhand to avoid arithmetic errors. Never assume — multiply out explicitly.
3. $\omega_1^2 - \omega_2^2 = 14400 - 6400 = 8000 \text{ rad}^2\text{ s}^{-2}$ — This is the quantity that determines how much energy is exchanged.
4. $\Delta E_k = \frac{1}{2} \times 4.0 \times 8000$ — [M1 — correct substitution with $I = 4.0$ kg m²]
5. $\Delta E_k = 2.0 \times 8000 = 16000 \text{ J}$ — [A1 — correct answer with units] The flywheel releases 16 kJ of energy as it decelerates.

Answer: $\Delta E_k = 16000 \text{ J}$ (16 kJ)

5. Real-World Applications of Flywheels

Flywheels appear in a wider range of engineering contexts than most students initially expect. The unifying thread is always the same: a process that delivers or demands energy in bursts, and a flywheel that bridges the gap between supply and demand.

• Internal combustion engines: the flywheel mounted on the crankshaft smooths the torque pulses from individual cylinder firings, ensuring steady rotation transmitted to the gearbox.
• Industrial punch presses and forging machines: a motor charges the flywheel continuously; the flywheel discharges its energy in a brief, high-power punch stroke, allowing a smaller motor to suffice.
• Pottery wheels: a heavy stone or concrete flywheel stores enough rotational energy to keep the wheel spinning smoothly between foot kicks, giving the potter consistent speed.
• Kinetic energy recovery systems (KERS): used in motorsport and some buses, a flywheel stores braking energy and releases it to assist acceleration, improving fuel efficiency.
• Uninterruptible power supplies (UPS): high-speed flywheels (spinning at tens of thousands of rpm in a vacuum) store electrical energy converted to rotational form, releasing it instantly if mains power fails.
• Steam engines: the flywheel was a defining feature of early steam engines, smoothing the single-acting piston stroke into continuous rotary motion for factory machinery.

Each application exploits the same physics: a large $I$ at a given $\omega$ stores a large $E_k$, and that energy can be released on demand. The engineering challenge is choosing the right combination of $I$ and $\omega$ for the power and duration required, while keeping the flywheel structurally safe at high rotational speeds.

6. Evaluating Flywheel Design: Advantages and Limitations

A well-designed flywheel is mechanically elegant: no chemical reactions, no phase changes, and no degradation over charge-discharge cycles. The energy is stored and retrieved with high efficiency, and the device can respond almost instantaneously to changes in load. These properties make flywheels attractive where rapid energy exchange is more important than long-duration storage.

However, flywheels carry genuine limitations that must be weighed in any evaluation. The energy stored scales with $\omega^2$, so high rotational speeds are needed for compact, high-energy designs — but high speeds create enormous centrifugal stresses in the material. A flywheel that fails at speed can disintegrate catastrophically, which is why high-performance flywheels require containment housings and careful material selection (carbon-fibre composites are used in modern KERS systems precisely because of their high strength-to-mass ratio).

Energy is also lost continuously to bearing friction and, in open designs, to air resistance. High-speed flywheels used for energy storage are therefore often run in a partial vacuum with magnetic bearings to minimise these losses. For long-duration energy storage (hours to days), electrochemical batteries or pumped hydro remain more practical — flywheels are best suited to short-duration, high-power applications.

7. Exam Technique: Getting Full Marks on Flywheel Questions

Flywheel questions at A level typically combine calculation with explanation or evaluation. The calculation marks are straightforward if you follow a consistent method; the explanation marks require precise physical language. Here is where most marks are dropped — and where you can gain a clear advantage.

For a 6-mark 'evaluate' question on flywheel suitability, structure your answer as: (1) state the relevant property of a flywheel (large $I$, high $\omega$, rapid response); (2) link it to the specific application context; (3) identify a limitation; (4) compare with an alternative if prompted; (5) reach a clear, justified conclusion. Examiners award marks for the quality of reasoning, not just for mentioning correct terms.

Every flywheel question, whether a short calculation or a 6-mark evaluation, traces back to the same two ideas: moment of inertia determines how strongly the flywheel resists speed changes, and rotational kinetic energy determines how much energy it can store and release. Secure those two ideas and the applications follow naturally.