Torque and the lever (equilibrium)
How effectively a force rotates something depends on the torque M=F·r (force times moment arm). A lever is in equilibrium when the torques on both sides are equal: F₁r₁ = F₂r₂. That is why a longer arm lets a smaller force balance a larger one. Change the forces and the arm lengths.
What just happened?
A large force on a short arm was balanced by a smaller force on a longer arm. The beam stays level because the two torques are equal.
Torque:
— the product of force and moment arm (the distance from the axis of rotation). The same force on a longer arm produces a greater torque. F — force (N), r — moment arm (m), M — torque (N·m).
Lever equilibrium condition:
The sum of torques turning it left equals the sum turning it right. When they balance, the beam does not rotate — it stays level.
Where to place the fulcrum?
The fulcrum (axis of rotation) separates the arms. Moving it closer to the larger force shortens that force's arm and reduces its torque — that is why you can lift a heavy object with a small force if you act on a long arm.
Why you need this for the exam:
M = F·r plus the condition ΣM = 0 solve problems about levers, balances, and beams. The trick: compute the torque of each force about the axis (force × arm) and set the sums on both sides equal.
Remember: at equilibrium the sum of torques to the left equals the sum to the right — F₁r₁ = F₂r₂. Torque is what counts, not force alone.
Theory & formulas
Torque
Force times the moment arm (the distance of the force's line of action from the axis of rotation). It is the torque, not the force alone, that determines how effectively something rotates.
Lever equilibrium
A lever is in equilibrium when the torques on both sides balance: That is why a longer arm lets a smaller force balance a larger one.
Notation: — torque, — force, — moment arm, subscripts — the two sides of the lever.
Frequently asked questions
›What is torque?
The product of the force and the length of its moment arm (the distance from the axis of rotation): M=F·r. It determines how effectively something rotates.
›How does a lever work?
It lets you balance or overcome a large force with a smaller force applied on a longer arm — because what counts is the torque M=F·r, not the force alone.
›Where should the fulcrum go?
Where the torques on both sides balance (F₁r₁=F₂r₂). Closer to the larger load if you want to lift it with a smaller force.
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