Moments Lab: Balance, Ladders & Centre of Mass
A free moments simulation with draggable masses, force sensors and Teacher / Student views.
Explore the principle of moments
This free moments simulation connects turning forces, equilibrium and centre of mass. Move several masses along a beam, investigate a ladder against a wall, or use force sensors to measure a plank. Teacher view shows the calculations; Student view keeps the given measurements and asks learners to work out the answers. Optional hints support the method.
How do you calculate a moment?
A moment is the turning effect of a force about a point. Calculate it using moment = force × perpendicular distance from the pivot to the force’s line of action. Force is measured in newtons, distance in metres and moment in newton metres (N m). Here g = 10 N/kg, so a 2 kg mass has a weight of 20 N.
For rotational equilibrium, the total clockwise moment equals the total anticlockwise moment. A massless seesaw with a 20 N weight 1.0 m from the pivot balances a 10 N weight 2.0 m on the other side: each produces 20 N m. Add every contribution when several weights act.
Seesaw: compare the turning effects
Drag masses onto the beam and move them in 0.1 m steps. Move the pivot to change their distances. The beam tips as a visual cue, while all calculations refer to the level beam. Equal moments return the display to horizontal. This display behaviour is a teaching convention: a perfectly frictionless knife edge does not itself provide a restoring moment.
Ladder: balance forces and moments
A stationary ladder requires horizontal force balance, vertical force balance and moment balance. Take moments about the foot to eliminate both floor forces. A smooth wall supplies a normal reaction but no friction. At a rough surface, static friction adjusts to the demand up to its limiting value μN.
Teacher view includes a button to find limiting equilibrium. With friction at both contacts, equilibrium alone does not determine every force; the model states the extra convention it uses. Student view asks for the floor reaction and required friction without displaying their numerical answers.
Centre of mass: use the sensor readings
The two sensors measure upward forces in newtons. Their sum equals the combined weight of the plank and any separate end load. Subtract the known end load to obtain the plank’s own weight, then divide by g for its mass. Taking moments about sensor A gives the position of the plank’s centre of mass.
Keep the plank and end load as separate masses. Adding an end load changes the sensor readings, but does not change the plank’s own centre of mass. The “Set sensor A to zero” button places the apparatus at the threshold of lift-off.
GCSE and A-level practice
Use the seesaw for GCSE Physics moments and balancing problems. The ladder and sensor investigations extend the same principle to A-level Physics and A-level Maths mechanics. Try Student view first, use a hint if needed, then switch to Teacher view to discuss the working.
Continue with all physics simulations, A-level mechanics questions or physics resources.