1. Rotation Rotation Variables 1 Rotation and Translation Angular Displacement Direction of Angular Displacement Calculation of Angular Displacement Comparison of Rotation to Translation

2. Rotation Rotation Variables 2 Translation Everything we have done in this class so far is classified as translation. Translation occurs when a particle or system displaces from one point to another in space. Objects that translate change their position. Rotation We will now discuss rotation. Rotation occurs when a particle or system turns about a single point. Objects that rotate change their angle.

3. Rotation Rotation Variables 3 Angular Displacement Angular displacement is a vector that determines the direction and magnitude of rotation or revolution of an object. Its magnitude is the angle through which the object rotated or revolved.

4. Rotation Rotation Variables 4 The magnitude of the angular displacement is the angle through which an object rotates or revolves Rotation is shown here

5. Rotation Rotation Variables 5 The magnitude of the angular displacement is the angle through which an object rotates or revolves Revolution is shown here

6. Rotation Rotation Variables 6 Angles have units of radians, revolutions or degrees. However, they have no dimension. To convert, we use the following factors

7. Rotation Rotation Variables 7 The direction of angular displacement is given by the right- hand rule This is the symbol for a vector pointing out of the page or screen This is the symbol for a vector pointing into the page or screen

8. Rotation Rotation Variables 8 A B 1.Point the fingers of your right hand in the direction of the vector A. 2.Curl your fingers toward the direction of the vector B. 3.The cross-product is given by the direction of your thumb. Right-hand Rule

9. Rotation Rotation Variables 9 For small angles ( ), we can find translational ( ) displacement from the radius vector ( ) and the angular displacement ( )

10. Rotation Rotation Variables 10 As we will learn later, the translational variables all have rotational counterparts. They are NameTranslationRotation or Angular Mass (Moment of Inertia) mI Positionr Velocityv Accelerationa Force (Torque)F EnergyKK MomentumpL

11. Rotation Rotation Variables 11 The equations relating these variables are NameEquationComment Mass (Moment of Inertia) N/A depends on the geometry of the object Displacement Velocity Acceleration Force (Torque) EnergyN/A there is no relationship Momentum

12. Rotation Rotation Variables 12 The equations using these variables are mathematically equivalent For instance