Rotation and Translation Angular Displacement Direction of Angular Displacement Calculation of Angular Displacement Comparison of Rotation to Translation

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.

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.

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

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

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

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

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

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

As we will learn later, the translational variables all have rotational counterparts. They are Name Translation Rotation or Angular Mass (Moment of Inertia) m I Position r Velocity v Acceleration a Force (Torque) F Energy K Momentum p L

The equations relating these variables are Name Equation Comment Mass (Moment of Inertia) N/A depends on the geometry of the object Displacement Velocity Acceleration Force (Torque) Energy there is no relationship Momentum

The equations using these variables are mathematically equivalent For instance