# Rotatum

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 derived from 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·m2/s3), 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:

$\mathbf{\Rho}=\frac{\mathrm{d}\mathbf{\tau}}{\mathrm{d}t}=\frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{\mathrm{d}\mathbf{L}}{\mathrm{d}t}\right)=\frac{\mathrm{d}^2\mathbf{L}}{\mathrm{d}t^2}=\frac{\mathrm{d}^2(I\cdot\mathbf{\omega})}{\mathrm{d}t^2}$

where $I$ is moment of Inertia and $\omega$ is angular velocity. If the moment of inertia isn't changing over time (i.e. it's constant), then:

$\mathbf{\Rho}=I\frac{\mathrm{d}^2\omega}{\mathrm{d}t^2}$

which can also be written as:

$\mathbf{\Rho}=I\zeta$

where ς is Angular jerk.