What Are Linear and Angular Velocity?

Date: 09/16/2004 at 14:16:28
From: Sang-duk
Subject: radians and linear and angular velocity confusion

What exactly is linear and angular velocity?  I know the formulas, 
s = rt and w = theta/r, but what do they mean?

Date: 09/16/2004 at 15:36:21
From: Doctor Schwa
Subject: Re: radians and linear and angular velocity confusion

Hi Sang-duk,

Linear velocity is how fast something moves: its distance divided by time.

Angular velocity is how fast something turns: its angle moved divided
by time.

For example, when a CD is spinning in a CD player, suppose it spins
200 times per minute.  Its angular velocity is 200 spins per minute,
or 200*360 degrees per minute, or 200*2pi radians per minute, or
200*2pi/60 radians per second, or ...

The CENTER of the CD has a linear velocity of zero: it's not going
anywhere!  If the edge is 6 cm away, then the edge of the CD spins
(2pi * 6) = 12pi cm per spin, so the linear velocity is 2400pi cm/minute.

Does that make sense?  The angular velocity is (spins or degrees or
radians) per minute while the linear velocity is (cm or m or feet or
inches) per minute.

Let me know if you still have questions!

- Doctor Schwa, The Math Forum
  http://mathforum.org/dr.math/