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## Centripetal Force Summary

A force that is… | will make a | or… |
---|---|---|

parallel to velocity | change speed (speed up) | accelerate (in the usual sense of the word) |

antiparallel to velocity | change speed (slow down) | decelerate (which is just another way to accelerate) |

perpendicular to velocity | change direction (turn) | accelerate centripetally (which is also just another way to accelerate) |

- A centripetal acceleration (
**a**)_{c}- occurs whenever a moving object changes direction
- does not change the speed of an object
- acts at right angles to the velocity at any instant
- is directed toward the center of a circle (center seeking)

- A centripetal force (
**F**)_{c}- is the force that makes a moving object change direction
- is not a particular force, but the name given to whatever force or combination of forces is responsible for a centripetal acceleration
- acts at right angles to the velocity at any instant
- is directed toward the center of a circle (center seeking)

- Directions in circular motion
- Velocity (
**v**) is tangential (lies on a tangent to the path). - Centripetal acceleration and centripetal force are centripetal (point toward the center of a circle).
- Centripetal acceleration is perpendicular to velocity.
- Centripetal force is parallel to centripetal acceleration.

- Velocity (
- Equations [with SI units]
- speed and velocity
*linear quantities**v*=**2π***r**T*Where…

*v*=speed [m/s] π = the mathematical constant *r*=radius of circular path [m] *T*=period of revolution [s] *angular quantities***v**=**ω**×**r**Where…

**v**=translational velocity vector [m/s] **r**=radius vector [m] **ω**=angular velocity vector [rad/s] - frequency and period
*linear quantities***ƒ =****1***T*Where…

*f*=frequency of revolution [Hz = 1/s = s ^{−1}]*T*=period of revolution [s] *angular quantities***ω =****2π****= 2πƒ***T*Where

**ω =****magnitude of angular velocity or angular frequency [rad/s]****π =****the mathematical constant***T*=**period of revolution [s]***f*=**frequency of revolution [Hz = 1/s = s**^{−1}] - centripetal acceleration
*linear quantities**a*=_{c}*v*^{2}**=****4π**^{2}*r**r**T*^{2}Where…

*a*=_{c}**centripetal acceleration [m/s**^{2}]*v*=**speed [m/s]***r*=**radius of circular path [m]****π =****the mathematical constant***T*=**period of revolution [s]***angular quantities***a**=_{c}−ω ^{2}**r**=**ω**×**v**Where

**a**=_{c}**centripetal acceleration vector [m/s**^{2}]**ω =****magnitude of angular velocity or angular frequency [rad/s]****r =****radius vector [m]****ω =****angular velocity vector [rad/s]****v =****translational velocity vector [m/s]**

- speed and velocity
- A centrifugal force…
- is a fictitious force (a.k.a. an apparent force or a pseudo-force)
- is not the result of an iteraction between objects
- ceases to exist when an object stops moving in a circle
- is an illusion experienced in a rotating reference frame
- appears to be directed away from the center of a circle (center fleeing)

- Circular motion in which the speed is constant is called uniform circular motion.