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Uniform Circular Motion


A particle P is said to be undergoing uniform circular motion if its radius vector in appropriate coordinates has the form (x(t),y(t),0), where

x(t)=Rcos(omegat)
(1)
y(t)=Rsin(omegat).
(2)
Uniform circular motion animation

Geometrically, uniform circular motions means that P moves in a circle in the xy-plane with some radius R at constant speed. The quantity omega is called the angular velocity of P. The speed of P is

 v=Romega,
(3)

and the acceleration of P has constant magnitude

 Romega^2=(v^2)/R
(4)

and is directed toward the center of the circle traced by P. This is called centripetal acceleration.

Ignoring the ellipticity of their orbits, planet show nearly uniform circular motion about the Sun. (Although due to orbital inclinations, the orbital planes of the different planets are not necessarily coplanar.)


See also

Angular Velocity, Circle, Ellipse, Simple Harmonic Motion

This entry contributed by David Terr

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Cite this as:

Terr, David. "Uniform Circular Motion." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/UniformCircularMotion.html

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