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Consider an object that moves from point *P* to *P*' along a
circular trajectory of radius *r* , as shown in Figure 7.2.

**Definition:** Tangential Speed

The **average tangential speed** of such an object is defined
to be the
length of arc, *s* , travelled divided by the time interval,
*t* :

= . | (11) |

v _{t} = .
| (12) |

s = r
| (13) |

v_{t} = r = r.
| (14) |

- The instantaneous tangential velocity
**vector**is always perpendicular to the radius vector for circular motion.

**Definition:** Tangential Acceleration

**Tangential acceleration** is the rate of change of tangential
speed. The
**average tangential acceleration** is:

= | |||

= |
r = r
| (15) |

a_{t}
| = | ||

= |
r
| (16) |

- The above formula is only valid if the angular velocity is
expressed in
**radians per second**. -
The direction of the tangential acceleration
**vector**is always parallel to the tangential velocity, and perpendicular to the radius vector of the circular motion.

10/9/1997