What your result means
A moment is the turning effect of one weight: its force multiplied by how far it sits from the pivot. Each side produces one, and they fight each other. Net torque is what is left over after the smaller cancels part of the larger — the amount actually available to turn the beam.
If the net is zero the beam stays wherever you left it. If not, the last figure gives the balance distance: where the right-hand mass would have to sit to make the two moments match. For a bolt or a spanner rather than a beam, the same quantity is what the torque calculator works out directly.
Why this one is different
Each side's moment is shown on its own before the net figure, which is what makes the balance legible: the same net torque can come from two small weights or two large ones nearly cancelling. A verdict says which way it tips and how hard, and the stage above tilts by the amount the numbers imply.
How it works
Weight alone does not decide a seesaw — leverage does. A force applied further from the pivot sweeps through more distance for the same rotation, so it does more work per degree and counts for more. Multiply force by distance and you get a moment; set the two moments equal and the beam balances, whatever the individual masses are.
Once the beam tilts, both lever arms shorten by the same cosine factor, so a beam that is out of balance stays out of balance all the way down — there is no angle at which it catches itself. How quickly it goes is a separate question: net torque divided by rotational inertia gives the angular acceleration, and inertia grows with the square of distance, so moving a mass outwards increases its moment but also makes the whole beam more sluggish. This simulator integrates that rotation step by step and stops the beam when its end reaches the ground.
How to use this simulator
- Set a mass and a distance for each side. Distances are measured from the pivot outwards.
- Press level the beam to release it from horizontal and watch which way it goes.
- Press balance it for me to move the right-hand mass to the exact balance distance.
- Then nudge that distance by a single centimetre — the beam tips again, which is why real balance scales are so sensitive.
Formula
balance condition: mₗ · rₗ = mᵣ · rᵣ
balance distance: rᵣ = ( mₗ · rₗ ) ÷ mᵣ
net torque: τₙₑₜ = ( mₗ · rₗ − mᵣ · rᵣ ) · g
rotation: α = τₙₑₜ ÷ I
- m — mass on that side, in kilograms
- r — distance from the pivot to that mass, in metres
- g — gravitational field strength, 9.80665 m/s²
- τ — moment, or torque, in newton-metres
- I — rotational inertia of beam plus masses, in kg·m², which sets how fast the tip happens but never which way
Example calculation
A 25 kg child sitting 1.8 m out, against a 70 kg adult at 0.6 m:
τᵣ = 70 × 9.80665 × 0.6 = 411.9 N·m
net = 441.3 − 411.9 = 29.4 N·m, left side down
balance rᵣ = ( 25 × 1.8 ) ÷ 70 = 0.643 m
Those are the simulator's starting values, and the panel shows exactly these figures. The child is nearly three times lighter yet still wins, because 4.3 cm of extra lever arm is all it takes.
Frequently asked questions
How can a light person balance a heavy one?
By sitting further from the pivot. Balance depends on mass multiplied by distance, not mass alone, so a 25 kg child at 1.8 metres exactly matches a 70 kg adult at 0.643 metres. The child has less weight but a longer lever arm, and the two products come out equal.
Why does a seesaw tip slowly at first and then faster?
The lever arm of each weight shrinks as the beam tilts, following the cosine of the tilt angle, but so does the arm of the opposing weight, so the net torque falls while the beam keeps turning. What you mostly see is the beam accelerating from rest: net torque divided by rotational inertia gives a small angular acceleration at first, and speed builds from there until the beam reaches the ground.
Does it matter where the pivot sits under the beam?
Yes, and this simulator assumes the pivot is under the centre of a uniform beam, so the beam's own weight is balanced and cancels out. Move the pivot off centre on a real seesaw and the longer side adds a permanent moment of its own, which has to be counted alongside the riders.
Related calculators
Assumptions & limitations
- The beam is uniform and pivoted at its centre. Its own weight therefore balances out and never appears in the moments.
- The pivot is frictionless. A real seesaw loses energy at the bearing, so it settles sooner than this one.
- Each mass is a point on the beam. No bodies leaning, bouncing or shifting weight mid-tip, which is how riders actually control a seesaw.
- Masses stay put. Nothing slides down the beam as it tilts, and nobody pushes off the ground.
- The beam stops dead at the ground. No bounce, and the tilt limit is fixed at 28° rather than taken from a real seat height.
Further reading
Our guide to force, work, energy and power explains why a longer lever arm does more work per degree of rotation, which is the reason moments multiply distance by force at all.
Sources & references
The moment convention, the balance condition and the rotational dynamics used here come from the following, all specific to levers and rigid-body rotation.
- OpenStax University Physics — static equilibrium, and the worked lever and seesaw cases
- OpenStax University Physics — Newton's second law for rotation, the torque and rotational inertia relationship behind the animation
- BIPM SI Brochure — the newton-metre as the coherent SI unit of moment of force
- NIST — standard acceleration of gravity, the exact 9.80665 m/s² used here