A balance beam is in equilibrium when the turning effects cancel: m1·d1 = m2·d2. Drag the sliders below to set each side's mass and its distance from the pivot, and watch the two moments decide whether the beam balances or tips.
Equilibrium & the Balance Beam
A beam is in balance when the turning effects cancel: τ = F·d = m·g·d on each side must be equal (Στ = 0). Drag the masses (or use the sliders) — bigger mass or longer arm means more torque and the beam tips that way.
What Is the Equilibrium Simulator?
The equilibrium simulator is a free interactive physics lab that runs in your browser — nothing to install and no sign-up. Change the masses and their distances on a balance beam and watch the principle of moments balance the beam. It reports Status, Left torque τ1, Right torque τ2, Net torque Στ and Support force as you drag the sliders.
| Control | Range | Step |
|---|---|---|
| Left mass | 0.1 – 5 kg | 0.1 |
| Left distance from pivot | 0.1 – 1.5 m | 0.1 |
| Right mass | 0.1 – 5 kg | 0.1 |
| Right distance from pivot | 0.1 – 1.5 m | 0.1 |
Why a Small Mass Far Out Can Balance a Big One
A light weight sitting far out on the beam can balance a heavy weight parked close to the pivot, and that surprises most people. The reason is that balance never depends on mass alone. What counts is the moment each side produces — the force times its perpendicular distance from the pivot. Because weight is mass times gravity, each side's turning effect is m·g·d. Distance pulls its full weight in that product, so a modest mass with a long lever arm competes directly with a bulky mass sitting near the middle.
Slide the four controls and watch the two moment readouts. The beam settles when the clockwise and anticlockwise moments cancel: m1·g·d1 = m2·g·d2. Since g is identical on both ends, it drops straight out, leaving the clean rule m1·d1 = m2·d2. Tip either product higher than the other and the status flips to tipping; match them and it reads balanced. Starting from a balanced beam, double the Left mass and you must halve the Left distance from pivot to bring it level again.
Full equilibrium asks for two things at once: the net force must be zero and the net moment about the pivot must be zero. On this beam the pivot's support already supplies whatever upward force is needed, so your whole job is matching the two moments. Push the idea further with the torque calculator, or line up your next build at the full simulation shelf.
Frequently asked questions
What is the principle of moments?
A pivoted beam balances when the total clockwise moment equals the total anticlockwise moment: m1·d1 = m2·d2 (the g's cancel). A moment is a force times its perpendicular distance from the pivot.
How can a small mass balance a bigger one?
By sitting further from the pivot. Balance depends on the product mass × distance, not on mass alone, so a small mass far out can match a large mass close in.
What are the conditions for equilibrium?
Two must hold at once: the net force is zero, and the net moment (torque) about any point is zero. On a balance beam that reduces to matching the two moments.
If I double a mass, what keeps the beam balanced?
Halve its distance from the pivot (or double the moment on the other side). The product mass × distance must stay equal on both sides.
References & formula source
- Halliday, Resnick & Walker — Fundamentals of Physics, Chapter 12 (Equilibrium and Elasticity).
- Young & Freedman — University Physics with Modern Physics, §11.1–11.2 (Conditions for Equilibrium; Torque).
- R. Nave — HyperPhysics, Georgia State University, "Torque and Rotational Equilibrium" section.
- Further reading: Mechanical equilibrium — Wikipedia