Question

What is the relationship between linear speed and angular speed?

Answer 1

`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`