Moment of a force


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 intensitythe forcewith 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


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 orbending 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 ofstatic 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 ⋅ ⋅ sin α


  •  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


  • 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:

  • 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 .


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.

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