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### More On Uniform Circular Motion

Newton's 1st Law of motion states that an object moving at constant speed will continue in that motion unless acted on by an outside force. A 'center seeking' force is required to cause an object to move in a circle. Centripetal means 'center seeking'. When someone (maybe even a lizard!) spins a ball attached to a rope horizontally about his head, it is a centripetal force transmitted through the rope from the muscles of the hand and arm that causes the ball to move in a circular path. Centripetal forces cause centripetal accelerations. In the special case of the Earth's circular motion around the Sun, or any satellite's circular motion around any celestial body; the centripetal force causing that motion is the result of the gravitational attraction between them.

 The arrows or vectors show the direction of the circular velocity (tangent to the circular path) and the circular acceleration caused by a centripetal force. Centripetal means center-seeking. Centripetal forces are always directed toward the center of the circular path. http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/circmot/ucm.html
Acceleration is the rate of change in velocity of an object. Velocity is determined by dividing the distance travelled by the time interval it took to cover that distance. In the special case of circular motion, the distance covered is the circumference of a circle or 2'pi'r. The time interval for an object to travel once around its circular path is called the period and is represented by T.

The equation for centripetal acceleration is:

 The equation for centripetal force is :

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