Rotatum
In physics, rotatum is the derivative of torque with respect to time. Expressed as an equation, rotatum Ρ is:
where τ is torque and is the derivative with respect to time .
The term rotatum is not universally recognized but is commonly used. This word is derived from the Latin word rotātus meaning to rotate. The units of rotatum are force times distance per time, or equivalently, mass times length squared per time cubed; in the SI unit system this is kilogram metre squared per second cubed (kg·m^{2}/s^{3}), or Newtons times meter per second (N·m/s).
Relation to other physical quantities
Newton's second law for angular motion says that:
where L is angular momentum, so if we combine the above two equations:
where is moment of Inertia and is angular velocity. If the moment of inertia isn't changing over time (i.e. it's constant), then:
which can also be written as:
where ς is Angular jerk.



Linear/translational quantities 

Angular/rotational quantities 
Dimensions 
1 
L 
L^{2} 
Dimensions 
1 
1 
1 
T 
time: t s 
absement: A m s 

T 
time: t s 


1 

distance: d, position: r, s, x, displacement m 
area: A m^{2} 
1 

angle: θ, angular displacement: θ rad 
solid angle: Ω rad^{2}, sr 
T^{−1} 
frequency: f s^{−1}, Hz 
speed: v, velocity: v m s^{−1} 
kinematic viscosity: ν, specific angular momentum: h m^{2} s^{−1} 
T^{−1} 
frequency: f s^{−1}, Hz 
angular speed: ω, angular velocity: ω rad s^{−1} 

T^{−2} 

acceleration: a m s^{−2} 

T^{−2} 

angular acceleration: α rad s^{−2} 

T^{−3} 

jerk: j m s^{−3} 

T^{−3} 

angular jerk: ζ rad s^{−3} 



M 
mass: m kg 


ML^{2} 
moment of inertia: I kg m^{2} 


MT^{−1} 

momentum: p, impulse: J kg m s^{−1}, N s 
action: 𝒮, actergy: ℵ kg m^{2} s^{−1}, J s 
ML^{2}T^{−1} 

angular momentum: L, angular impulse: ΔL kg m^{2} s^{−1} 
action: 𝒮, actergy: ℵ kg m^{2} s^{−1}, J s 
MT^{−2} 

force: F, weight: F_{g} kg m s^{−2}, N 
energy: E, work: W kg m^{2} s^{−2}, J 
ML^{2}T^{−2} 

torque: τ, moment: M kg m^{2} s^{−2}, N m 
energy: E, work: W kg m^{2} s^{−2}, J 
MT^{−3} 

yank: Y kg m s^{−3}, N s^{−1} 
power: P kg m^{2} s^{−3}, W 
ML^{2}T^{−3} 

rotatum: P kg m^{2} s^{−3}, N m s^{−1} 
power: P kg m^{2 }s^{−3}, W 
