Constant-power rotational acceleration ($\frac{I}{2}\frac{d{\omega }^2}{dt}=P-\gamma {\omega }^2$)

A rigid body with moment of inertia $I$, constant driving power $P$ and linear resisting torque $-\gamma \omega$ has an exponential approach of ${\omega }^2$ to $P/\gamma$. The ideal drive requires torque $P/\omega$, so starting from rest is a limiting energy model with singular initial torque.