# Work, Energy, Power, Torque, etc. (relationships)

{units} are provided for information only
The following relationships apply to any and all consistent units, both metric and Imperial
The symbol ᶜ refers to radians

## Linear:

Momentum (p) = m.a.t = m.v {kg.m/s}

Force (F) = m.a {kg.m/s²}

Energy (U) = F.d = m.a.d {kg.m/s² . m}

Potential Energy (Uᴾ) = m.a.d {kg.m²/s²}

Kinetic Energy (Uᴷ) = ½.m.v² {kg.m²/s²}

Deformation Energy (Uᴰ) = ½.m.a.y {kg.m/s² . m}

Work (W) = Energy {kg.m²/s²}

Power (P) = m.a.d / t {kg.m/s² . m / s}

Energy = Work = Power . t = Momentum . v

Where:
m = mass {kg}
a = acceleration {m/s²}
d = distance {m}
y = deformation {m}
v = velocity {m/s}
t = time {s}

## Rotary:

Inertia (I) = ⅖.m.R² {kg.m²}

Torque (T) = m.α.R² {kg . ᶜ/s² . m²}

Energy = ½.I.ω² = ½ . ⅖.m.R² . ω² = ½ .⅖ . m.(ω.R)² [= ⅕.m.v²] {kg . ᶜ²/s² . m²}

Work = 2π.T {ᶜ . kg.m²/s²}

Power = 2π.N.T = ω.T {ᶜ/s . kg.m²/s²}

Energy = 2π . Work = 2π.t . Power = (2π)² . Torque

Where:
m = mass {kg}
α = angular acceleration (ᶜ/s²)
v = rotational velocity at the surface of the mass {m/s}
ω = angular velocity {ᶜ/s}
t = time {s}
2π.t = angular period {ᶜ.s}

## Orbital Power:

Orbital power in a satellite, may be established from its momentum multiplied by the potential (gravitational) acceleration induced by its force-centre:
P = m₂.v.g (kg . m/s . m/s² = kg.m²/s³ = J/s)
where:
g = G.m₁/R²
'm₁' is the force-centre mass
'm₂' is the satellite mass
'v' is the satellite velocity
'g' is the force-centre's potential acceleration
This means that whilst a satellite's energy is constant throughout its orbit, its power will vary.