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Units for other physical quantities are derived from this set as needed. In English Engineering Units, the pound-mass and the pound-force are distinct base units, and Newton's Second Law of Motion takes the form = where is the acceleration in ft/s 2 and g c = 32.174 lb·ft/(lbf·s 2).
A newton is defined as 1 kg⋅m/s 2 (it is a named derived unit defined in terms of the SI base units). [1]: 137 One newton is, therefore, the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force.
This is convenient because one pound mass exerts one pound force due to gravity. Note, however, unlike the other systems the force unit is not equal to the mass unit multiplied by the acceleration unit [11] —the use of Newton's second law, F = m ⋅ a, requires another factor, g c, usually taken to be 32.174049 (lb⋅ft)/(lbf⋅s 2).
Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1,000 newtons, which is the weight one would expect on Earth from an object with a mass slightly greater than 100 kilograms.
The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass. The kilogram-force leads to an alternate, but rarely used unit of mass: the metric slug (sometimes mug or hyl) is that mass that accelerates at 1 m·s −2 ...
The slug is defined as the amount of mass that accelerates at 1 ft/s 2 when one pound-force is exerted on it, and is equivalent to about 32.2 pounds (mass). The kilogram-force is a non-SI unit of force, defined as the force exerted by a one-kilogram mass in standard Earth gravity (equal to 9.80665 newtons exactly).
The unit of substance in the FPS system is the pound-mole (lb-mol) = 273.16 × 10 24. Until the SI decided to adopt the gram-mole, the mole was directly derived from the mass unit as (mass unit)/(atomic mass unit). The unit (lbf⋅s 2 /ft)-mol also appears in a former definition of the atmosphere.
In engineering and physics, g c is a unit conversion factor used to convert mass to force or vice versa. [1] It is defined as = In unit systems where force is a derived unit, like in SI units, g c is equal to 1.