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 centerseeking.
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 :
