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Consider an object moving in a circle of radius *r* with constant
angular velocity. The tangential *speed* is constant, but the
direction of the tangential *velocity vector* changes as the
object
rotates.

**Definition:** Centripetal Acceleration

**Centripetal acceleration** is the rate of change of
tangential velocity:

= | (17) |

**Note: **

- The direction of the centripital acceleration is always inwards along the radius vector of the circular motion.
- The magnitude of the centripetal acceleration is related to
the tangential speed and angular velocity as follows:
*a*_{c}= =*r*.(18) - In general, a particle moving in a circle experiences both
angular
acceleration and centripetal accelaration. Since the two are always
perpendicular, by definition, the magnitude of the net acceleration
*a*_{ total}is:*a*_{ total}= = .(19)

**Definition:** Centripetal Force

**Centripetal force** is the net force causing the centripetal
acceleration of an object
in circular motion. By
Newton's Second Law:

= m.
| (20) |

F_{c} = ma_{c} = m = mr.
| (21) |

10/9/1997