Moment of force. Equilibrium conditions and dynamics

09/04/2026

The online moment of force simulations on this page will allow you to study how moments act on objects in different static and dynamic situations. We will discover how the moment of force is calculated, what are the equilibrium conditions of forces and moments for a system to be stable and how moments act in a dynamic system

What is the moment of force

The moment of force, also known as moment or torque, is a physical quantity that describes the tendency of a force to cause a rotation around a specific point or axis. It is produced by the application of a force at a given distance from the point of rotation.

Calculation of the moment of force

The moment of force is calculated by multiplying the magnitude of the force by the perpendicular distance from the point of rotation to the line of action of the force. Mathematically, it is expressed as:

Moment = force × distance × sin(θ).

Where:

Force is the magnitude of the applied force.

Distance is the perpendicular distance from the point of rotation to the line of action of the force.

θ is the angle between the direction of the force and the line joining the point of rotation to the point of application of the force.

The moment of force is measured in a unit called newton-meter (Nm) in the International System (SI).

The moment of force can be positive or negative, depending on the direction of rotation it induces. If the moment is positive, it indicates a clockwise rotation, while if it is negative, it indicates a counterclockwise rotation.

Equilibrium conditions. Equilibrium of forces and equilibrium of moments

For a body to be in complete equilibrium, two main conditions must be met: equilibrium of forces and equilibrium of moments.

Equilibrium of forces

The equilibrium of forces implies that the vector sum of all forces acting on the object must be equal to zero, which ensures that there is no linear motion.

Moment equilibrium

On the other hand, moment equilibrium requires that the algebraic sum of all the moments of forces acting on the object with respect to a given point or axis also equals zero; this means that there is no net tendency to rotate.

Moment of force in dynamics

In dynamics, the moment of forces plays a crucial role as it is directly linked to the angular acceleration and rotational inertia of an object. When a force acts on a rigid body at a certain distance from an axis of rotation, it generates a moment that can produce a rotation. The magnitude of the angular acceleration experienced by the object depends not only on the applied force and the distance to the axis, but also on the mass distribution of the object, which is known as the moment of inertia. The moment of forces is therefore responsible for the fact that bodies such as wheels, pendulums or gears can start, stop or modify their rotational motion.

Applications of the moment of force

The moment of force has numerous practical applications in fields such as engineering, mechanics, architecture and physics, where they are used for the design of structures, the determination of the stability of objects and the analysis of rotational motions.

Explore the exciting STEM world with our free, online, simulations and accompanying companion courses! With them you’ll be able to experience and learn hands-on. Take this opportunity to immerse yourself in virtual experiences while advancing your education – awaken your scientific curiosity and discover all that the STEM world has to offer!

Moment of force simulations

Balance
Bridge
Lever

Balancing Act

Play with objects on a seesaw to learn about balance. Test what you’ve learned with the balance challenge game and verify that equilibrium is achieved when there is equilibrium of forces and equilibrium of moments. .

Suspension bridge

Lever

A lever is a tool that allows us to transmit force using a bar and a fulcrum. See what force is required to balance the mass depending on the distance to the fulcrum.

Door
Arm
Bridge II

Turning a door

In this simulation, the moment required to rotate the door is fixed. Observe how the force to be applied varies when moving the handlebar or changing the angle of application of the force. How to minimize the force required?

Rocker arm

In this simulation, different masses can be placed in various positions on the rocker arm. See how by changing the masses and the distances to the center of each side, different balanced configurations can be achieved.

Suspension bridge

Giants of science

“If I have seen further, it is by standing on the shoulders of giants”

Isaac Newton

Archimedes

287 a.C.

–

212 a.C.

Archimedes established fundamental principles of mechanics and hydrostatics, including the famous Archimedes’ principle of buoyancy in fluids

“Give me a place to stand, and I will move the world”

Daniel Bernoulli

1700

–

1782

Daniel Bernoulli formulated Bernoulli’s principle and developed fundamental theories in fluid mechanics and gas dynamics

“Nature is always economical in its means”

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Gottfried Wilhelm Leibniz

1646

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1716

Gottfried Wilhelm Leibniz was one of the founders of infinitesimal calculus, created modern mathematical notation, and contributed to mechanics and optics with groundbreaking theories

“Music is the hidden exercise of arithmetic of the soul, which does not know it is calculating.”

Augustin-Louis Cauchy

1789

–

1857

Augustin-Louis Cauchy formalized mathematical analysis, providing rigor to calculus and function theory, influencing mathematical physics

“Rigor in mathematics is the key to understanding physical phenomena”

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Test your knowledge

What is the equilibrium of forces and how is it determined in a system?

The equilibrium of forces occurs when the vector sum of all forces acting on an object is zero, meaning the object experiences no acceleration and remains at rest or in constant motion. To determine this, all acting forces are analyzed in both magnitude and direction, using vector decomposition and summation. This concept is fundamental for understanding static structures, like bridges and buildings, as well as everyday problems such as placing objects on a table without them falling. It also serves as the basis for studying stability and safe design in engineering and applied physics.

What is the relationship between moments of force and rotational equilibrium?

The moment of force, or torque, measures a force’s tendency to produce rotation around a point or axis. Rotational equilibrium occurs when the sum of all moments acting on a body is zero, so there is no net rotation. This means that opposing forces, even if not equal, can balance if their moments compensate each other. Understanding this relationship allows us to analyze levers, beams, and complex mechanical systems, and it is crucial for solving practical engineering and mechanics problems.

How is it that an object can remain stable even when forces act in different directions?

Even if an object is subject to several forces pulling in different directions, it remains stable if these forces combine so that their net effect is zero. For example, a picture frame hanging from two nails doesn’t move because the tensions balance out. It’s fascinating to realize that forces are present, but thanks to how they interact, no visible movement occurs.

Does it make sense that changing the position of a force can alter equilibrium even if its magnitude is the same?

Yes, and this is due to the concept of moment: the effect of a force depends on both its magnitude and its distance from the pivot point. That’s why moving a force closer or further from the axis can create or eliminate rotation, even if the force itself remains identical. This principle is essential in levers and pulleys and explains why certain configurations are more efficient for lifting loads.

And how can we use levers or bars to lift heavy objects without increasing the force?

Through mechanical advantage: by strategically placing the fulcrum and adjusting the lengths of the lever arms, a small force can produce the same effect as a larger one. This shows that understanding the equilibrium of forces and moments not only explains stability but also allows us to manipulate objects efficiently, as in cranes, scissors, or wheelbarrows.