Uniform Circular Motion:
* When an object moves in a circle at a constant speed, it is said to undergo uniform circular motion.

* The time it takes the object to make one revolution is called the object's period P. If the object is moving at a constant speed, then

* For uniform rotational motion, the angle the object makes with the x-axis is simply provided that at time zero the object is on the x-axis. Here w is the angular velocity of the object's rotation about the center, and is equal to either: w = v/r or w = 2p/P


* The object's location at any moment - its equation of motion - relative to the center of rotation is given by

where i and j with the little hats are the unit vectors in the x and y directions.

* The object's velocity is easily found by taking the derivative of its location with respect to time.

* This velocity is always tangent to the circle or equivalently, is always perpendicular to

* The object's acceleration is easily found by taking the derivative of its velocity with respect to time.

* The direction of the object's acceleration is opposite , i.e., directed towards the center of motion.

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