Every nameplate, tachometer and datasheet in a plant is written in rpm — revolutions per minute, the symbol $n$. Every equation in your course is written in $\mathrm{rad/s}$. The two never share a value, and the bridge between them is worth memorising in one piece: $\omega = \dfrac{2\pi n}{60}$. Revolutions become radians ($\times 2\pi$); minutes become seconds ($\div 60$). As one number that is a division by 9.549 — but keep it as $2\pi/60$ and you will never forget which way it goes.

The period $T$ is the other way in: the time in seconds for exactly one revolution. One revolution is $2\pi$ radians, so $\omega = \dfrac{2\pi}{T}$ — omega equals two pi over T. That is $\omega = \theta/t$ with the angle already filled in for you. And a nameplate speed converts straight to a period: at $n$ rpm one revolution takes $T = 60/n$ seconds.

Put a radius on it and you get the rim speed the same way: $v = \dfrac{2\pi r}{T}$ — one circumference of $2\pi r$ metres, covered every $T$ seconds, where $r$ is the radius in metres and $v$ is in $\mathrm{m/s}$. If a rotational answer ever looks wrong by roughly six, you have found this bridge unpaid.