Counter-Rotating Flywheel Pair: Cancelling Gyroscopic Reaction Torque

Flywheel Rig

A single spinning flywheel is mounted in the vehicle. Yaw the vehicle and watch the reaction torque arrow spike.

Flywheel spin 4000 rpm

Flywheel mass (each) 12 kg

Vehicle yaw rate Ω 20°/s

Live Readouts

Net angular momentum |L|0 kg·m²/s

Reaction torque |τ|0 N·m

Stored energy (total)0 kJ

How it works

A flywheel energy-storage unit doesn't just hold kinetic energy — it holds angular momentum, L = Iω, pointing along its spin axis. If the vehicle or spacecraft carrying it yaws at rate Ω about an axis perpendicular to that spin axis, the mount must supply a torque to force the spin axis to keep turning with the body:

τ = Ω × L
|τ| = |Ω| |L| sin(angle between Ω and L)

By Newton's third law the flywheel pushes an equal and opposite reaction torque back into the frame — a real engineering headache for single-flywheel energy storage on spacecraft, ships and buses, since it fights every turn.

The fix used on real systems: mount two identical flywheels spinning in opposite directions on parallel axes. Their individual angular momenta L₁ = +Iω and L₂ = −Iω cancel exactly, so the net L — and therefore the net reaction torque τ = Ω × L_net — drops to zero, while total stored kinetic energy ½Iω² is additive, not cancelling, so the pair stores twice the energy of one wheel for zero net gyroscopic disturbance.

Flywheel spin — sets ω, the rotor speed in each wheel.
Flywheel mass — sets the moment of inertia I = ½mr² of each disk (radius fixed at 0.32 m).
Vehicle yaw rate Ω — how fast the chassis is turning; this is what excites the reaction torque.
Mode toggle — switch between one flywheel (torque spikes with every turn) and a counter-rotating pair (torque stays near zero).

Net angular momentum L Reaction torque τ = Ω×L

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