# Angular Kinematics

Objectives:

• Define:
• Relative and absolute angular position
• Angular displacement
• Average angular velocity
• Instantaneous angular velocity
• Average angular acceleration
• Instantaneous angular acceleration
• Name units of measurement for above definitions
• Explain the relationship between angular and linear motion
• Define:
• Tangential acceleration and explain its relationship to angular acceleration
• Centripetal acceleration and explain its relationship to angular velocity and tangential velocity

Linear and Angular Quantities

```                           ANGULAR DISPLACEMENT
AVE ANGULAR VELOCITY = ---------------------------
CHANGE IN TIME
```
```                            CHANGE OF ANGULAR VELOCITY
AVE ANGULAR ACCELERATION = ---------------------------
CHANGE IN TIME

```
• Slope of angular position versus time equals angular velocity
Running Example

• Connection of Linear and Angular Velocity:Golf example

V = ω * r
Discuss how weight and length of golf clubs relates to the distance the club should hit.

• Tangential Acceleration: The component of of linear acceleration tangent to the circular path of a point on a rotating object

aT = α * r

• Centripetal Acceleration: The linear acceleration directed toward the axis of rotation

ar = ω 2 r

Hammer throw example