---
title: "Centrifugal Governor Interactive Lab | Sandbox Physics"
description: "Why does the sleeve rise as the spindle speeds up? Between the travel stops, faster rotation opens the flyball arms farther. The equal upper and lower links pull the sliding sleeve upward as they open. Once the sleeve reaches a stop, its position stays fixed and the contact force changes with speed instead."
canonical_url: "https://sandboxphysics.com/labs/centrifugal-governor/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/centrifugal-governor/"
last_modified: "2026-10-24"
---

Rotating flyballs · A rising sleeve

# Centrifugal Governor

**Why does the sleeve rise as the spindle speeds up?** Between the travel stops, faster rotation opens the flyball arms farther. The equal upper and lower links pull the sliding sleeve upward as they open. Once the sleeve reaches a stop, its position stays fixed and the contact force changes with speed instead.

Drag a blue flyball or change the spindle speed. Watch the sleeve rise between two physical stops, then compare its low-speed, freely raised and travel-limited positions.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Two equal point masses rotate at a prescribed speed on equal, massless upper and lower links. Both pivot pairs have the same finite radial offset. The sleeve is massless and frictionless, with ideal lower and upper stops. Each setting shows a steady position. Engine feedback, hunting, friction, impact and structural limits are omitted.

Physics tutorial

## How the flyballs lift a sleeve

**Background** A rotating shaft carries two equal flyballs. Their upper and lower links connect the balls to a sliding sleeve.

**Why it matters** The same linkage can turn a change of speed into a visible displacement that a real governor can use to move a valve.

Start with the essentials

- **Focus question**: Does increasing spindle speed always raise the sleeve farther?
- **One-sentence intuition**: Between the stops, greater speed opens the arms and raises the sleeve. At a stop, the contact force changes instead of the sleeve position.

### Core mathematical model

#### Finite pivot offsets and sleeve travel

$$
r=a+L\sin\theta,\quad y_s=H-2L\cos\theta
$$

Both pivot pairs lie at radial distance a from the spindle. The upper and lower links each have length L.

#### The free steady position

$$
\omega^2(a+L\sin\theta)=g\tan\theta
$$

This relation balances the two force components when the sleeve is not touching a stop. Setting the offset to zero gives the ideal on-axis conical-pendulum limit.

#### The force from a stop

$$
F_s=m\left[g-\omega^2r\cot\theta\right]
$$

The upward reaction is positive. It vanishes in the free range; at the lower and upper stops it points up and down respectively. Mass refers to one of the two equal balls.

### Common difficulties

#### A speed sensor is not a closed control loop

**Typical misconception** The moving sleeve on this page proves that an engine will regulate its own speed stably.

**Better mental model** This page prescribes speed and calculates a steady position. Engine torque, load, valve feedback and transient dynamics are needed to study regulation and hunting.

#### New settings prepare a new steady motion

**Typical misconception** The instantaneous change of angle is a prediction of how the real apparatus accelerates.

**Better mental model** The model compares exact steady configurations. It does not integrate the forces during preparation, so no settling time or transient power is reported.

### Run the experiment

1. 01

   #### Grab the ball

   Pause, then drag a blue ball outward or upward in the main scene.

   **What to observe:** The linked sleeve rises as the arms open. The spindle speed updates to the corresponding steady setting.

2. 02

   #### Try both travel limits

   Select Lower stop, Sleeve raised and Upper stop. Open More measurements.

   **What to observe:** The sleeve moves only between its stops. Outside that interval the stop carries a nonzero vertical reaction.

3. 03

   #### Change gravity and mass

   Try Moon gravity, then change Mass in the collapsed group.

   **What to observe:** Gravity changes the speed needed to hold a given angle. At fixed speed and geometry, equal changes of ball mass scale the forces without changing the steady position.

Physical conclusion

A governor's geometry converts speed to sleeve position; travel stops and engine feedback are separate parts of the physics.

Scientific sources

[Richard Fitzpatrick · The conical pendulum](https://farside.ph.utexas.edu/teaching/301/lectures/node88.html) · [J. C. Maxwell · On Governors (1868)](https://www.maths.ed.ac.uk/~v1ranick/papers/maxwell1.pdf) · [TecQuipment · Flyballs and sleeve](https://www.tecquipment.com/governors)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)