What is the relationship between linear speed and angular speed?

##v=omegaR##
Linear velocity ##v## is equal to the angular speed ##omega## times the radius from the center of motion ##R##.
We can derive this relationship from the arclength equation
##S=thetaR## where ##theta## is measured in radians.
Start with
##S=thetaR##
Take a derivative with respect to time on both sides
##d S/dt=d theta/dtR##
##d S/dt## is linear velocity and ##d theta/dt## is angular velocity
So we’re left with:
##v=omegaR##