radian per second squared

Angular acceleration is the unit of changing rotation, and motor drives are where it earns its keep. A machine commanded from rest to 1,800 rpm in one second undergoes about 188 rad/s², since 1,800 rpm is 188.5 rad/s, and the torque bill follows immediately from $\tau = I\alpha$: spinning a rotor of $I = 0.5$ kg·m² up that hard takes about 94 N·m before any load is even attached. Drive commissioning menus usually ask for the ramp in rpm per second instead, and 1 rpm/s is $\pi/30 \approx 0.105$ rad/s², the same conversion rpm always carries. The rotational-mechanics solvers on this site work in rad/s² throughout, so ramp specifications convert on the way in.

The slowest angular acceleration anyone routinely quotes belongs to the planet. Tidal friction lengthens the day by roughly 1.8 milliseconds per century, and pushing that published figure through the definition, a fractional change of 1.8 ms in 86,400 s spread over a century of seconds acting on $\omega = 7.29 \times 10^{-5}$ rad/s, gives a spin-down near 5 × 10⁻²² rad/s². A motor start and the braking of the Earth sit twenty-four orders of magnitude apart on the same unit.