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Model check
The science
What you see
Left: the governor from the side. Two balls hang on arms from the spindle; as it spins they swing outwards and lift the sleeve. Right: the same balls from above on their circle, with the speed v = omega r. Arrows show the weight mg and the centrifugal term m omega^2 r (seen from the rotating frame).
Equilibrium
Balance of the tension, the weight and the required centripetal force gives tan(theta) = omega^2 r / g with r = L sin(theta), hence cos(theta) = g / (omega^2 L). Below the critical speed omega_0 = sqrt(g / L) the arms rest on the lower stop; here the stops are at 8 and 68 degrees as in the 3D model, which uses the same equilibrium function.
A speed-independent law
The depth of the balls below the pivot is L cos(theta) = g / omega^2, whatever the ball mass: a heavier ball needs a larger force but also provides it, so only speed sets the angle. That is why a governor measures speed.
Dynamics
The angle obeys theta'' = omega^2 sin(theta) cos(theta) - (g/L) sin(theta) - c theta'. Linearised about equilibrium the arms oscillate at omega sin(theta); damping makes them settle. The checks compare the simulated settling and period with these formulas.
Simplifications
The two balls and arms are treated as an ideal rigid conical pendulum (massless arms, point balls, pivot on the axis); the lower links and sleeve are only drawn, not part of the dynamics, and there is no friction or engine load. The 3D model's pivot offset is a visual detail that this simplified equilibrium does not include.