The idea. A force on a lever tries to turn it about the pivot (the fulcrum). The turning effect is the torque, the force multiplied by its perpendicular distance from the pivot:

τ = F × d

The beam is in rotational equilibrium (the principle of moments) when the clockwise and the anticlockwise torques are equal. If they are not, the beam turns towards the side with the bigger torque, and the bigger the difference the faster it speeds up. A tiny difference (under 0.5%) is held by the friction at the pivot.

First-class lever (the pivot is between the load and the effort: a seesaw, scissors, a crowbar, pliers). The load (on the left) turns the beam anticlockwise; the effort (on the right) turns it clockwise. The weight of the beam acts at the pivot (a uniform beam, 10 kg), so it has no turning effect.

m_load g d_load = m_effort g d_effort

The g cancels, so a 20 kg load 3 m from the pivot (60 kg m) is balanced by 15 kg at 4 m, or by 60 kg at 1 m. The effort can be smaller than the load (mechanical advantage above 1), equal to it, or bigger, depending on the arms.

Second-class lever (the load is between the pivot and the effort: a wheelbarrow, a nutcracker, a bottle opener, a door). The load pushes down and turns the beam clockwise. The effort pulls up at the far end and turns it anticlockwise. The beam is treated as light, so its own weight is ignored. For balance:

F_effort d_effort = m g d_load, so F_effort = m g d_load / d_effort

Because the effort is farther from the pivot than the load, the effort force is always smaller than the weight of the load.

Mechanical advantage. The ratio of the force on the load to the effort force is the mechanical advantage. At balance it equals the ratio of the arms: F_load/F_effort = d_effort/d_load. For the nutcracker preset it is 5, and the handle moves 5 times as far as the nut. A first-class lever can have a mechanical advantage below 1, equal to 1 or above 1. A second-class lever always has one above 1.

What to do. (1) Choose the lever and set the masses, forces and distances (or drag them). (2) Work out the torques by hand and type them in; for the second-class lever also work out the effort that would just balance the load. (3) Choose what you think the beam will do. (4) Press Release the beam. The page shows the true torques, checks your prediction and your answers (to 1%), and the beam moves.

Why it takes time to move. The beam has a moment of inertia (for the first-class lever I = Σmd² + ML²/12 for the beam, and for the second-class lever I = md² plus a light beam), and the angular acceleration is α = τ_net/I. The beam stops against the supports at 12 degrees. When it tilts, all the lever arms shrink by the same factor, cos θ (the forces stay vertical), so this does not change which side wins. There is a small amount of friction at the pivot.

Things to try. (1) Which is more important for the torque, the mass or the distance? (2) Find three different settings that balance. (3) “Almost balanced” for the first-class lever differs by 1.3%. What does the beam do, and how long does it take? (4) In the second-class tab, move the effort closer to the load. What happens to the effort needed? (5) A third-class lever has the effort between the pivot and the load (tweezers, a fishing rod, your forearm). What would its mechanical advantage be?