Linear Velocity
Now imagine that you are riding on a carousel next to someone, and you are sitting on the outside. Both of you have the same angular velocity, but you have to travel a longer distance than your friend who is sitting on the inside.
How do you find this linear velocity?
If an object moves with a constant linear velocity for a period of time, then the distance the object travels is given by the equation:
, where 
is the linear velocity and t is time.
Solving for :
Using the formula for the length of a circular arc, s = r 
:
Linear velocity is therefore defined as:
, or 
, where 
is angular velocity given in 