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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.
One newton equals one kilogram metre per second squared. Therefore, the unit metre per second squared is equivalent to newton per kilogram, N·kg −1, or N/kg. [2] Thus, the Earth's gravitational field (near ground level) can be quoted as 9.8 metres per second squared, or the equivalent 9.8 N/kg.
The SI has special names for 22 of these coherent derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m 2), the SI derived unit of area; and the kilogram per cubic metre (kg/m 3 or kg⋅m −3), the SI derived unit of density.
[1] An SI derived unit is a named combination of base units such as hertz (cycles per second), newton (kg⋅m/s 2), and tesla (1 kg⋅s −2 ⋅A −1) and in the case of Celsius a shifted scale from Kelvin. Certain units have been officially accepted for use with the SI.
newton meter squared per kilogram squared (N⋅m 2 /kg 2) shear modulus: pascal (Pa) or newton per square meter (N/m 2) gluon field strength tensor: inverse length squared (1/m 2) acceleration due to gravity: meters per second squared (m/s 2), or equivalently, newtons per kilogram (N/kg) magnetic field strength
The metre, kilogram, second system of units, also known more briefly as MKS units or the MKS system, [1] [2] [3] is a physical system of measurement based on the metre, kilogram, and second (MKS) as base units. Distances are described in terms of metres, mass in terms of kilograms and time in seconds.
For example, 1 m/s = (1 m) / (1 s) is the coherent derived unit for velocity. [ 1 ] : 139 With the exception of the kilogram (for which the prefix kilo- is required for a coherent unit), when prefixes are used with the coherent SI units, the resulting units are no longer coherent, because the prefix introduces a numerical factor other than one.
The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2). It should not be confused with the second moment of area , which has units of dimension L 4 ([length] 4 ) and is used in beam calculations.