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/
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