Circular Motion vs Linear Motion Equations

C = 2πr
v = Cω = 2πrω
ω = 1 / T

ω = angular speed (revolutions/s)
v = linear speed (m/s)
r = radius of circular path (m)
C = circumference of circular path (m)
T = period of circular motion = time to complete one revolution (s)
2π ≈ 6.283

These equations use revolutions per second (rev/s) units for angular speed.

RPM (revolutions per minute) is also a common unit. Divide by 60 to convert from RPM to rev/s.

It is also common to use radians instead of revolutions. If you find examples using radians, you can use 1 rev = 2π radians to convert.
(Conveniently, if you’re using radians, ω = v/r)

Consider the reciprocal relationship between angular speed, ω, and period, T. If an object has an angular speed of 2 revolutions per second, both of the following are true:

$\omega = \cfrac{2 rev}{1 s}$

$T = \cfrac{1 s}{2 rev} = \cfrac{0.5 s}{1 rev}$

Also consider how we can compare our constant velocity equation from kinematics to our circular motion equations:

$v = \cfrac{\Delta x}{\Delta t}$

$v = \cfrac{C}{T}$

For one revolution around a circular path, the distance, Δx, is the circumference, C. The time, Δt, is the period, T.