Two important aspects must be known and taken into account before being able to define the correct moment of a force. The first of them, **force** , is an **action** such that when it is applied to a certain body it is capable of **modifying** its **speed** , causing an **acceleration** or a certain change in its **shape** . The second definition that interests us is that of **force** , which is a **vector magnitude** , in other words, a force that, in addition to a **module** , also has a direction and a sense. The **moment** is in charge of seeing **intensity**the **force**with which you try to turn a rigid body. The moment may increase if the force that is applied increases as if the **distance** from the axis to the point of **application** of the force increases.

**Unit:**Nm**Formula:**M = F⋅r⋅sin α

## What is the moment of a force?

The **moment of a force** with respect to a given point is a **vector ****magnitude** that is obtained from the vector **product** of the **vector** that is in the position of the point of **application** of the **force** .

- Definition
- How to calculate the moment of a force
- Interpretation of the moment of a force
- Examples

## Definition

The **moment of a force** in relation to a point, shows us to what **extent** the **capacity** can be given in a **force** or system of forces to change the state of the **rotation** of the body around an **axis** that passes through a certain point. . The moment of a force generally produces an **angular acceleration** , in other words, it produces a change in the speed of **rotation** in the body on which it is applied and is a characteristic **magnitude** in the elements that are subjected to **torsion** , such as on machinery shafts or**bending such** as in beams.

It is also called the moment of a force, or **torque** as it is also known, to that **vector magnitude** which is a measure of the **rotational** capacity that said force is capable of producing in a given body, when this body has the capacity to **rotate** around a point that is considered a **fixed point** . The moment of a force is a concept, it is a widely used concept in the area of **physics** and it helps us to solve **lever** problems when it is necessary to find out **distances** or **forces** . It is also very useful to be able to solve problems of**static** and **balance** in general .

## How to calculate the moment of a force

The **moment of a force** or M →, is also known by the name of **torque** , **dynamic moment** or is sometimes called only **moment. **This moment is a vector magnitude that is responsible for measuring the capacity of a force to be able to alter the **speed of rotation of** a body. Its module can be obtained through the following expression:

**M = F ****⋅ ****r ****⋅ ****sin α**

Where:

**M**refers to the modulus of the moment of a**force F →**which is applied on a body. Its unit in the international measurement system is the**newton**per meter (N · m).**F**refers to the modulus of force. Its**unit**in the international measurement system is the**newton**.**r**is the module of the**position****vector**that is responsible for joining the center or axis of rotation with the point of origin of the applied force. The unit that represents it in the international measurement system is the**meter**.**α**is the angle formed between**F →**and**r →.**

The value of the moment of a force can also be obtained as:

**M = F ****⋅d**

Where:

**M**represents the modulus of the moment of a**force F →**that is applied on a body.**F**is the module of the**force**applied to the**body**.**d**is the distance between the**axis**of**rotation**and the**line**on which the force F rests.

## Interpretation of the moment of a force

According to what has been studied, the moment of a **force** does not provide a measure of the effectiveness of the forces to be able to produce a certain **movement** of **rotation** or rotation of a body. The **intensity** or the **moment** of a force will always depend on the intensity that the acting **force** has. Depending on the results, there may be different **variations** at the moment, which are:

- A
**greater force**corresponds to a**greater moment**and reciprocally. - The
**greater the arm**, the**greater the moment**and reciprocally. - It can be obtained
**greater**,**less**or**equal** - You get a
**higher** - The moment is
**less**.

## Examples

Some examples of the moment of a force are as follows:

- A practical example of the moment of a force can be seen in the
**mechanical wrench**that is used to tighten nuts and similar elements. The**longer**the wrench arm, the easier it is to tighten or loosen the nuts.