Moments & the lever
About this app
Moment of a force M=F·r about a pivot with the perpendicular lever arm shown; the lever law on a seesaw with moment equilibrium ΣM=0 and the sense of rotation in colour.
The basics
The moment of a force describes its turning effect about a point. It is M = F·r⊥, where r⊥ is the perpendicular lever arm, the shortest distance from the pivot to the line of action of the force. Depending on its position, a force turns clockwise or counterclockwise, which sets the sign of the moment. A body is in rotational equilibrium when the sum of all moments is zero: ΣM = 0. For a two-armed lever this gives the law of the lever, F₁·r₁ = F₂·r₂. A small force on a long arm balances a large force on a short arm.
What you see
A beam is pivoted at its centre. Every load on the beam creates a moment; the app draws the perpendicular lever arm as a dashed line and colours the sense of rotation. Loads left of the pivot turn counterclockwise, loads on the right turn clockwise. A panel shows the resultant moment ΣM and the direction in which the beam tips. The beam visibly tilts as long as it is not balanced.
Things to try
Add loads, drag them along the beam or change force and distance with the sliders. Try to balance a large load near the pivot with a small load far out. The “Balance it out” button adjusts the values so that ΣM = 0; afterwards compare the products F·r on both sides.
Frequently asked questions
- How do you calculate the moment of a force?
- The moment about a point is M = F·r⊥, force times perpendicular lever arm. The lever arm is the distance between the pivot and the line of action of the force, which is not always the distance to the point of application. The unit is the newton metre (N·m).
- What does the law of the lever say?
- A lever is balanced when the moments on both sides are equal: F₁·r₁ = F₂·r₂. A force on a lever arm twice as long only needs to be half as large. The law of the lever is a special case of the equilibrium condition ΣM = 0.
- What is the difference between the lever arm and the distance to the point of application?
- The lever arm is the perpendicular distance from the pivot to the line of action. If a force acts at an angle, the lever arm is shorter than the distance to its point of application. Sliding a force along its line of action does not change its moment.
- What can I change in the lever app?
- You can add and remove loads, drag them along the beam and set their force and distance with sliders. The app shows the resultant moment and the sense of rotation. A button balances the seesaw automatically.
Subject: Engineering mechanics
More from Engineering mechanics
- Bending stress & moment of inertia
- Düsenjet bis v_max (3D)
- Energy & oscillation
- Truss analysis (method of joints)
- Equilibrium & support reactions
- Kinematics
- Kinetics & Newton's second law
- Forces & vector addition
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