Circular Motion and Acceleration

Date: 12/03/1999 at 05:07:52
From: Ben Chadwick
Subject: Circular motion

How can an object experiencing circular motion always be accelerating 
toward the center if the distance from the center is constant?

Date: 12/03/1999 at 13:04:01
From: Doctor Rick
Subject: Re: Circular motion

Hi, Ben.

Circular motion is confusing, I know. We must distinguish "circular" 
concepts from "linear" concepts. If an object maintains constant 
distance from the center, we say that it has zero "radial velocity" 
and zero "radial acceleration" because its radial velocity is 
constant. These are "circular concepts." But the object still has 
non-zero "linear acceleration," which we just call acceleration.

Acceleration (linear acceleration) means deviation from constant 
velocity. Constant velocity means motion at constant speed in a 
constant direction. An object in circular motion is constantly 
changing direction, and thus it is accelerating. The direction of this 
change in motion (acceleration) is toward the center.

If the object stops accelerating - if, for instance, you were swinging 
it on a string and the string were to break - it would move in a 
straight line tangent to the circle. Its distance from the center (or 
what had been the center) would increase.

If you compare the motion of the object in circular motion with this 
tangent-line motion of an unaccelerated object, you will see that the 
circular motion causes it to be closer to the center than it would 
have been if it were not accelerated. Thus, it is accelerating "toward 
the center."

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