In physics, rotatum is the derivative of torque with respect to time. Expressed as an equation, rotatum Ρ is:
 ${\vec {P}}={\frac {d{\vec {\tau }}}{dt}}$
where τ is torque and ${\frac {\mathrm {d} }{\mathrm {d} t}}$ is the derivative with respect to time $t$.
The term rotatum is not universally recognized but is commonly used. This word is derived from the Latin word rotātus meaning to rotate.^{[citation needed]} 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:
 $\mathbf {\tau } ={\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}$
where L is angular momentum, so if we combine the above two equations:
 $\mathbf {\mathrm {P} } ={\frac {\mathrm {d} \mathbf {\tau } }{\mathrm {d} t}}={\frac {\mathrm {d} }{\mathrm {d} t}}\left({\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}\right)={\frac {\mathrm {d} ^{2}\mathbf {L} }{\mathrm {d} t^{2}}}={\frac {\mathrm {d} ^{2}(I\cdot \mathbf {\omega } )}{\mathrm {d} t^{2}}}$
where $I$ is moment of Inertia and $\omega$ is angular velocity. If the moment of inertia is not changing over time (i.e. it is constant), then:
 $\mathbf {\mathrm {P} } =I{\frac {\mathrm {d} ^{2}\omega }{\mathrm {d} t^{2}}}$
which can also be written as:
 $\mathbf {\mathrm {P} } =I\zeta$
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 rads^{−1} 

T^{−2} 

acceleration: a m s^{−2} 

T^{−2} 

angular acceleration: α rads^{−2} 

T^{−3} 

jerk: j m s^{−3} 

T^{−3} 

angular jerk: ζ rads^{−3} 

M 
mass: m kg 
weighted position: M ⟨x⟩ = ∑ m x 

ML^{2} 
moment of inertia: I kgm^{2} 


MT^{−1} 

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

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

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