To bring any body into rotational motion, it is necessary to apply a moment of force to it. This article discusses what kind of physical quantity it is, by what formula it is calculated, and in what units of measurement it is customary to express the moment of force in the SI system.
The moment of force as a physical quantity
For any mechanical system in which there is an axis of rotation, the action of an external force not acting directly on the axis will lead to the appearance of a moment of force. Mathematically, it is expressed by the following formula:
M¯ = r¯ * F¯.
It can be seen from the expression that we are talking about the vector quantity M¯, which is equal to the product of the vectors r¯ (directed from the axis to the point of application of force) and F¯.
According to the rule of the gimlet, the value of M¯ is directed perpendicular to the plane formed on the vectors r¯ and F¯, in the direction of twisting of the gimlet. This direction is considered to be positive (+ M).
A moment of force characterizes the ability of an external force to rotate a body about an axis. For example, acting on a doorknob creates a much greater moment than applying a similar force near the hinges.
What are the units of torque?
This question is easy to answer if you look at the formula that is given in the previous paragraph. It can be seen that the units of distance (r¯) are multiplied by units of force (F¯). Since the first value is measured in meters in the SI system, and the second in newtons, it turns out that the moment of force will be expressed in meters per newton or, as is customary to write, in newtons per meter (N * m).
You can see that the units N * m correspond to work, that is, joules. However, the value of M is not expressed in joules, because in its physical sense it is not work, but represents only a means (opportunity) to do this work, which is expressed by the following equality:
A = M * θ, where θ is the angle of rotation in radians.
This expression allows you to get the moment M in other units: joules per radian or J / rad. For example, writing M = 30 J / rad means that applying the moment M, at which the system rotates by 1 radian, will cause it to complete work of 30 joules.