Uniform Circular Motion: Fc and ac

(Illustration)

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Uniform circular motion is an interesting mix of one- and two-dimensional concepts.  For uniform circular motion the speed of the object must be constant.  This is the uniform in uniform circular motion.  So is an object moving in a circle with a constant speed accelerating?  Yes!  Why?  The velocity is changing with time.  Watch the above animation (position is shown in meters and time is shown in seconds)Restart.  The above animation depicts an object moving in a circle at a constant speed.  To determine the acceleration we need to consider the change in velocity for a change in time.  

Since the speed does not change in time what does change in time?  It is the direction that changes with time.  Recall that velocity is a direction and a magnitude and either/both can change with time.  Where does the change in velocity point?  Towards the center of the circle.  Since the object is accelerating, this motion must be due to a force (or a set of forces, a net force) that points solely towards the center of the circle (Note: if the motion is non-uniform circular motion the net force can point in another direction. ).  This direction---towards the center of the circle---is called the centripetal or center-seeking direction.  It is often also called the radial direction, since the radius points from the center of the circle out to the object (the net force points in the in the opposite direction).  

Therefore, for uniform circular motion, the net force always points towards the center of the circle, no matter the cause. Despite the fact that the velocity and the force (and therefore the acceleration) point in changing directions as time goes on.  However, we get around this by defining the centripetal or radial direction and the tangential direction (the direction tangent to the circle).  These directions change, but the velocity is always tangent to the circle and the net force is always pointing towards the center of the circle. The following animation, shows v and a as the object undergoes uniform circular motion.