In physics meets a lot of different values, each of which has its own unit of measure. Arbitrary selection of these units greatly complicates the calculations, as in formulas, expressing the relationship between different physical quantities, appear the numerical coefficients, depending only on the choice of units.

Thus, an arbitrary choice of units of all the physical formulas necessary to write with some coefficients of proportionality k. For example, the formula for Newton's second law should be written in the form F=k₂ma, and the formula for power F on the path segment S in the form A=k₂FS and t. d.

However, in most formula of these coefficients can be eliminated, t. e. make them equal to one, if you enter arbitrary units for some physical quantities, adopted for the main, and units of other physical quantities output from the formulas. So, the mechanics can be taken as base quantities length, a lot, time for them to choose units (for example, meter, pounds, second), units and other mechanical values derived from formulas. Print, for example, the units of force and work.

 In the formula for Newton's second law F=k₁ma the coefficient k₁ will be equal to one, if weight, equal to one, and acceleration, equal to one, power is also equal to one. Having units of mass and acceleration, you can choose the unit of force so, this condition fulfilled. Then the formula for Newton's second law can be written k₁: F=ma. Will pick up now we need a unit of force. To do this, substitute in the place of m and a few of them with abbreviated names and perform algebraic steps as above numbers, and over the names:

F= 1 kg*1 m/s²= 1 kg *m/s².

Take the result per unit of force and we call this unit a Newton, and the expression kg*m/s²let's call the dimension of Newton. The result word can be expressed as: Newton (N) such a force is called, which mass in 1 kg accelerates in 1 m/s². So,

1 N=1 kg *m/s².

Similarly for the unit of work will receive

A=FS=1 N*1 m=1 N*m=1kg*m²/with²=1 j (Joule).

If the value of, looking for which unit, not expressed in an explicit form, it, considering the formula as an equation, need to find this value in letter form, and then to substitute known units. For example, suppose you want to display the speed unit from the formula s=vt Then write,

v=s/t= 1  m/1s=1 m/s.

Let us now state the rule of inference of physical units. To display a new unit of any physical quantity, need: 1) to find the formula, containing this value, in which the units of all other quantities known; 2) algebraically find the formula from the literal expression for this quantity; 3) in the resulting expression to substitute all of the known units with their dimensions; 4) to complete all the required algebraic steps as above numbers, and over dimensions; 5) to take the result for the desired unit and give it a name.

For example print is now a unit of power:

1)      Select formula: A=Nt; 2) we find from this formula N: N=A/t; 3) the substitution unit of work and time: N=1J/1C=(1 kg*m²/with²)/1with; 4) action: N=1kg*m²/with³; 5) accept this result for unit of capacity and give it the name watt (W): 1Int=1 kg*m²/with³.

Those units, which are set arbitrarily and independently from each other, for example, according to the international agreement, are called primary, and then, which are derived from formulas, known as derivatives (from the main). A set of basic units derived from them are called derived units, system of units.

Was, that to produce a system of mechanical units, it is advisable to install three main units, all other output from the formulas, in the examples above, the base units were: unit of length — 1m, mass unit — 1 kg and time unit 1C. Here the short name of m, kg, with dimensions are called fundamental units. The result of action on these dimensions, showing, as derived unit turned out to be major, is called the dimension of a derived unit.

Obviously, changing the main unit (for the same physical quantities, adopted for the main) or choosing other physical quantities as the main, you can get many different systems of units. Since the physical formula written without coefficients k, calculations will give the correct result only in the case, when all numeric values will be substituted in the same system of units.

At present, the calculations should use the International system of units, short — SI (system international). It is a single universal system, connecting the mechanical unit, heat, electrical and other physical quantities. It is built on seven core units:

1) unit of length — 1 meter (m);

2) mass unit — 1 pounds (kg);

3) time unit 1 second (with);

4) unit temperature — 1 Calvin (To);

5) the unit of current is 1 amps (And);

6) unit of luminous intensity — 1 Candela (CD);

7) unit of amount of substance — 1 mol (mol).

Precise definitions of these units are given below in the presentation of the relevant material.