 # Rotatum Redirected from 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 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·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:

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