Expert: Paul Klarreich - 12/18/2006

Question
I need to know the formula for angular speed i know that the linear speed is 15cm/second and the radius is 45 cm

Answer
Questioner:  Kendra
Category:  Calculus
 
Subject:  Angular Speed
Question:  I need to know the formula for angular speed i know that the linear

speed is 15cm/second and the radius is 45 cm
 
.....................................
Hi, Kendra,

If your object is moving about a circle with radius  r, and its velocity  ds/dt = v, then it takes it t = 2pi r/v  seconds to complete a circumference.

The circumference is  2pi r.
The time needed for one full rotation is C/v = 2pi r/v.

The angle swept out in that time is 2 pi.  So the angular speed will be:  [@ is the symbol for theta here.]

[USE A COURIER FONT TO VIEW THIS.]

       Angle swept out  
d@/dt = ----------------
        elapsed time

        2 pi      2 pi v
d@/dt = -------- = ------- = v/r
       2pi r/v    2 pi r

That's it:  Angular speed, sometimes written as omega (I don't know how to make one of those on this computer) is:

d@/dt = v/r

In this case d@/dt = 15/45 = 1/3 radian per second.

There is a good discussion at http://en.wikipedia.org/wiki/Angular_speed
Mostly I checked that site to make sure I didn't blow it --it has been a long time since freshman physics.