A relation between linear and agular velocities?

Question

A relation between linear and agular velocities?

Answer 1

v = rw

v= velocity m/s, radius of circular motion and w is angular speed in radians per sec

Answer 2

Jorge-

The relationship between linear variables and rotational variables is "easy"...

linear = rotational * radius or rotation, so...

Linear velocity = rotational velocity * radius

-Fred

Answer 3

Angular velocity has units of radians/second which can be expressed as revolutions/second since each revolution is 2pi radians.  So

Multiply the angular velocity in radians/second by

1 revolution/2pi radians and you and you get revolution/second.  Each revolution travels one circumference = 2pi*r  So the 2pi in the numerator cancels with the 2pi in the denominator and you get angular velocity*r= linear velocity as long as angular velocity is expressed in radians/second.