Centimetre–gram–second System of Units - Definition of CGS Units in Mechanics

Definition of CGS Units in Mechanics

In mechanics, the CGS and SI systems of units are built in an identical way. The two systems differ only in the scale of two out of the three base units (centimetre versus metre and gram versus kilogram, respectively), while the third unit (second as the unit of time) is the same in both systems.

There is a one-to-one correspondence between the base units of mechanics in CGS and SI, and the laws of mechanics are not affected by the choice of units. The definitions of all derived units in terms of the three base units are therefore the same in both systems, and there is an unambiguous one-to-one correspondence of derived units:

(definition of velocity)

(Newton's second law of motion)

(energy defined in terms of work)

(pressure defined as force per unit area)

(dynamic viscosity defined as shear stress per unit velocity gradient).

Thus, for example, the CGS unit of pressure, barye, is related to the CGS base units of length, mass, and time in the same way as the SI unit of pressure, pascal, is related to the SI base units of length, mass, and time:

1 unit of pressure = 1 unit of force/(1 unit of length)2 = 1 unit of mass/(1 unit of length·(1 unit of time)2)

1 Ba = 1 g/(cm·s2)

1 Pa = 1 kg/(m·s2).

Expressing a CGS derived unit in terms of the SI base units, or vice versa, requires combining the scale factors that relate the two systems:

1 Ba = 1 g/(cm·s2) = 10-3 kg/(10-2 m·s2) = 10-1 kg/(m·s2) = 10-1 Pa.