engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

and

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, ''g''_c is a unit conversion factor used to convert

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...

or vice versa. It is defined as :

g_\text = \frac

In unit systems where force is a

derived unit SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate ...

, like in

SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...

s, ''g''_c is equal to 1. In unit systems where force is a primary unit, like in

imperial and US customary measurement systems The imperial and US customary measurement systems are both derived from an earlier English system of measurement which in turn can be traced back to Ancient Roman units of measurement, and Carolingian and Saxon units of measure. The US Customa ...

, ''g''_c may or may not equal 1 depending on the units used, and value other than 1 may be required to obtain correct results. For example, in the

kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...

(KE) formula, if ''g''_c = 1 is used, then KE is expressed in

foot-poundal The foot-poundal (symbol: ft-pdl) is a unit of energy, introduced in 1879, that is part of the Absolute English system of units, which itself is a coherent subsystem of the foot–pound–second system. Edward F. Obert, Thermodynamics, McGraw-Hill ...

s; but if ''g''_c = 32.174 is used, then KE is expressed in

foot-pound The foot-pound force (symbol: ft⋅lbf, ft⋅lbf, or ft⋅lb ) is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a fo ...

Motivations

According to

Newton's second law Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion ...

, the

''F'' is proportional to the product of mass ''m'' and acceleration ''a'': :

F \propto ma

or :

F = K ma

If ''F'' = 1

lbf The pound of force or pound-force (symbol: lbf, sometimes lbf,) is a unit of force used in some systems of measurement, including English Engineering units and the foot–pound–second system. Pound-force should not be confused with pound-m ...

, ''m'' = 1 lb, and ''a'' = , then :

1~\text = K \cdot 1~\text \cdot 32.174~\frac

Leading to :

K = \frac = 0.03108~\frac

''g''_c is defined as the

reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another pol ...

of the constant ''K'' :

g_\text = \frac = 32.174~\frac

or equivalently, as :

g_\text = \frac

Specific systems of units

References

{{Reflist Equations