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# 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/"dt"R##

##d S/"dt"## is linear velocity and ##d theta/"dt"## is angular velocity

So we're left with: ##v=omegaR##