Rotation Variables Rotation and Translation Angular Displacement Direction
Rotation Variables Rotation and Translation Angular Displacement Direction of Angular Displacement Calculation of Angular Displacement Comparison of Rotation to Translation 1
Rotation Variables 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. 2 Objects that rotate change their angle.
Rotation Variables 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. 3
Rotation Variables The magnitude of the angular displacement is the angle through which an object rotates or revolves 4 Rotation is shown here
Rotation Variables The magnitude of the angular displacement is the angle through which an object rotates or revolves 5 Revolution is shown here
Rotation Variables Angles have units of radians, revolutions or degrees. However, they have no dimension. To convert, we use the following factors 6
Rotation Variables The direction of angular displacement is given by the righthand rule This is the symbol for a vector pointing out of the page or screen 7 This is the symbol for a vector pointing into the page or screen
Rotation Variables Right-hand Rule 1. Point the fingers of your right hand in the direction of the vector A. A B 2. Curl your fingers toward the direction of the vector B. 3. The cross-product is given by the direction of your thumb. 8
Rotation Variables For small angles ( ), we can find translational ( ) displacement from the radius vector ( ) and the angular displacement ( ) 9
Rotation Variables As we will learn later, the translational variables all have rotational counterparts. They are Name Translation Mass (Moment m of Inertia) Position r Velocity v Acceleration a Rotation or Angular I Force (Torque) F 10 Energy K K Momentum p L
Rotation Variables The equations relating these variables are Name Equation Mass (Moment N/A of Inertia) Comment depends on the geometry of the object Displacement Velocity Acceleration Force (Torque) Energy Momentum 11 N/A there is no relationship
Rotation Variables The equations using these variables are mathematically equivalent For instance 12
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