The official unit of angular velocity is in radians/second, but it can be expressed in several different ways.
A wheel spins at 5rad/s. This is pretty straightforward:
A wheel spins around 5 times per second. We can think of this in two different ways:
This is the angular velocity measured in revolutions per second, so we can convert it to rad/s by multiplying by :
"Turns per second" is sometimes referred to as the frequency. When we're given the frequency then :
A wheel takes 4 seconds to turn around once. This is referred to as the period of the wheel's rotation, and is given in units of s/rev. If we flip it upside-down, we get the frequency: We can then convert it to radians as above: Or more generally, This is probably the trickiest thing in these problems, because it looks like you're being given . Remember that is a duration, the time between some initial and final event, the time during which the wheel is speeding up or slowing down.