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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.
In some contexts, the term "pound" is used almost exclusively to refer to the unit of force and not the unit of mass. In those applications, the preferred unit of mass is the slug, i.e. lbf⋅s 2 /ft. In other contexts, the unit "pound" refers to a unit of mass. The international standard symbol for the pound as a unit of mass is lb. [8]
The constants listed here are known values of physical constants expressed in SI units; that is, physical quantities that are generally believed to be universal in nature and thus are independent of the unit system in which they are measured. Many of these are redundant, in the sense that they obey a known relationship with other physical ...
The pound-force provides an alternative unit of mass: one slug is the mass that will accelerate by one foot per second squared when acted on by one pound-force. [58] An alternative unit of force in a different foot–pound–second system, the absolute fps system, is the poundal, defined as the force required to accelerate a one-pound mass at a ...
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).
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 ]
Therefore, the spring constant k, and each element of the tensor κ, is measured in newtons per meter (N/m), or kilograms per second squared (kg/s 2). For continuous media, each element of the stress tensor σ is a force divided by an area; it is therefore measured in units of pressure, namely pascals (Pa, or N/m 2, or kg/(m·s 2).