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### Uniform Circular Motion

• For an object to maintain the same speed while moving in a circle, its velocity must constantly be changing-the object has an acceleration.
• The formula for acceleration if you have uniform circular motion (the same speed throughout the circle):
|

a

| =  | → v |2

r
.
• The acceleration vector always points from the object to the center of the circle.
• The velocity vector is always tangential to the circle.
• Remember: in the above equation, those are the magnitudes of the vectors, since the direction of both acceleration and velocity must constantly be changing.
• A revolution is one complete circuit of the circle.
• The circumference of a circle is 2πr and the speed is |v|, so the time it takes for one revolution is
T = 2πr

 | → v |
.

## Uniform Circular Motion

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