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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).
Systems of measure either define mass and derive a force unit or define a base force and derive a mass unit [1] (cf. poundal, a derived unit of force in a mass-based system). A slug is defined as a mass that is accelerated by 1 ft/s 2 when a net force of one pound (lbf) is exerted on it. [2]
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).
The SI unit of force is the newton (symbol N), which is the force required to accelerate a one kilogram mass at a rate of one meter per second squared, or kg·m·s −2.The corresponding CGS unit is the dyne, the force required to accelerate a one gram mass by one centimeter per second squared, or g·cm·s −2. A newton is thus equal to ...
Outside the SI system, other units of mass include: the slug (sl), an Imperial unit of mass (about 14.6 kg) the pound (lb), a unit of mass (about 0.45 kg), which is used alongside the similarly named pound (force) (about 4.5 N), a unit of force [note 3] the Planck mass (about 2.18 × 10 −8 kg), a quantity derived from fundamental constants
In unit systems where force is a derived unit, like in SI units, g c is equal to 1. In unit systems where force is a primary unit, like in imperial and US customary measurement systems , 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. [ 2 ]
Relation to SI units gram per millilitre g/mL ≡ g/mL = 1000 kg/m 3: kilogram per cubic metre (SI unit) kg/m 3: ≡ kg/m 3 = 1 kg/m 3: kilogram per litre kg/L ≡ kg/L = 1000 kg/m 3: ounce (avoirdupois) per cubic foot oz/ft 3: ≡ oz/ft 3: ≈ 1.001 153 961 kg/m 3: ounce (avoirdupois) per cubic inch oz/in 3: ≡ oz/in 3: ≈ 1.729 994 044 × ...