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Torque has the dimension of force times distance, symbolically T −2 L 2 M and those fundamental dimensions are the same as that for energy or work. Official SI literature indicates newton-metre , is properly denoted N⋅m, as the unit for torque; although this is dimensionally equivalent to the joule , which is not used for torque.
The amount of torque needed to cause any given angular acceleration (the rate of change in angular velocity) is proportional to the moment of inertia of the body. Moments of inertia may be expressed in units of kilogram metre squared (kg·m 2) in SI units and pound-foot-second squared (lbf·ft·s 2) in imperial or US units.
The jump in acceleration equals the force on the mass divided by the mass. That is, each time the mass passes through a minimum or maximum displacement, the mass experiences a discontinuous acceleration, and the jerk contains a Dirac delta until the mass stops.
The SI units for the torque constant are newton meters per ampere (N·m/A). Since 1 N·m = 1 J, and 1 A = 1 C/s, then 1 N·m/A = 1 J·s/C = 1 V·s (same units as back EMF constant). The relationship between K T {\displaystyle K_{\text{T}}} and K v {\displaystyle K_{\text{v}}} is not intuitive, to the point that many people simply assert that ...
Acceleration has the dimensions of velocity (L/T) divided by time, i.e. L T −2. The SI unit of acceleration is the metre per second squared (m s −2); or "metre per second per second", as the velocity in metres per second changes by the acceleration value, every second.
Change in angular velocity per unit time rad/s 2: T −2: Area: A: Extent of a surface m 2: L 2: extensive, bivector or scalar Area density: ρ A: Mass per unit area kg⋅m −2: L −2 M: intensive Capacitance: C: Stored charge per unit electric potential farad (F = C/V) L −2 M −1 T 4 I 2: scalar Catalytic activity concentration
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 ).
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.