Moment of force (Torque)

Dimension – [N ∙ m] (Newton per meter) or multiple values ​​[kN ∙ m]

The analogue of the moment of force is the moment of a couple of forces.

A prerequisite for the occurrence of the moment is that the point relative to which the moment is created should not lie on the line of action of the force.

Definition

The moment is defined as the product of the force F and the lever h:

M (F) = F × h

The shoulder of force h is defined as the shortest distance from the point to the line of action of the force.

For example, a force of 7 kN applied at a distance of 35 cm from the point in question gives the moment

M = 7 × 0,35 = 2,45 kNm.

Example of moment of force

The most obvious example of a moment of force is the turning of a nut with a wrench.

Nuts are wrapped by rotation, for this purpose a moment is applied to them, but the moment itself occurs when our wrench influences our force.

Of course, you intuitively understand that in order to tighten the nut harder, you must take the key as far as possible from it.

In this case, applying the same force, we get a large amount of moment by increasing its shoulder (h₂>h₁).

The shoulder is the distance from the center of the nut to the point of application of force.

Moment arm

Consider the procedure for determining the leverage h of the moment:

Let point A and some arbitrary force F be given, whose line of action does not pass through this point. It is required to determine the moment of force.

Show the line of action of the force F (dashed line)

From the point A we draw the perpendicular h to the line of action of the force

The length of the segment h is the shoulder of the moment of force F relative to point A.

The moment is considered positive if its rotation occurs counterclockwise (as in the figure).

It is so accepted that the signs of the moment and the angular displacement created by it coincide.

Examples of the calculation of the moment of force

The force is perpendicular to the axis of the rod

The distance between points A and B is 3 meters.

Moment of force relative to point A:

M(A) = F × AB = F × 3m

The force is at an angle to the axis of the rod

Moment of force relative to point B:

M(B) = F × cos30° × AB = F × cos30° × 3m

Know the distance from the point to the line of force

Moment of force relative to point B:

M(B) = F × 3m