What is the relationship between linear speed and angular speed?

1 Answer
Jul 17, 2015

Answer:

#v=omegaR#

Explanation:

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#