1. Rotational Motion Comparison of Angular Motion with One-dimensional Horizontal Motion Distance traveled is replaced by the angle traveled around the circle. Velocity is replaced by Angular Velocity. Acceleration is replaced by Angular Acceleration.

2. Comparison of Angular Motion with One-dimensional Horizontal Motion Rotational Motion

3. Any two points on a rigid rotating object have the same angular speed and angular acceleration. If the points moved at different rates, the rotating object would become distorted and change shape. Rotational Motion

4. Any two points on a rigid rotating object, at different distances from the axis of rotation, have DIFFERENT tangential speeds and tangential accelerations. One point must travel a larger distance  s, and must travel a faster tangential speed, or it will lag behind. Rotational Motion

5. Tangential Speed (V T ) is the instantaneous linear speed of an object traveling a linear distance  s along a circular path. The instantaneous linear speed of a point rotating about an axis. Rotational Motion

6. Tangential Speed (V T ) is the instantaneous linear speed of an object traveling a linear distance  s along a circular path. Tangential speed of an object is dependent on its angular speed and distance from the axis of rotation. Equation: Units: Rotational Motion

7. Tangential Acceleration (a T ) is the rate of change in tangential speed. The instantaneous linear acceleration of a point rotating about an axis. Tangential acceleration of an object is dependent on its angular acceleration and distance from the axis of rotation. Equation: units: Rotational Motion

8. Centripetal acceleration (a c ) is the acceleration of an object caused by its change in direction around an axis of rotation. It caused by a centripetal force F c and is directed toward the center of the circle along the radius.  V = V f – V i for extemely small values of  t approaching zero. Using tip-to-tail method.  V = a c directed toward center. Rotational Motion

9. Centripetal acceleration (a c ) is the acceleration of an object caused by its change in direction around an axis of rotation.

10. Rotational Motion Centripetal acceleration (a c ) is the acceleration of an object caused by its change in direction around an axis of rotation. Equation: units:

11. Tangential and Centripetal Acceleration Tangential a T and centripetal a C acceleration are perpendicular to each other. Tangential acceleration a T is a measure of a change in speed. Centripetal acceleration a C is a measure of change in direction.

12. Tangential and Centripetal Acceleration To find total acceleration of object, can use Pythagorean Theorem because Tangential a T and centripetal a C accelerations are perpendicular to each other.