Rotational Motion Rotational Inertia – inertia is how an object resists changing its motion so rotational inertia is how much an object resists changing its rotating motion Applying torque will change the rotational inertia of an object The greater the distance between an object’s center of mass and the axis that it rotates on, the greater the rotational inertia

Rotational Inertia Demo short pendulum vs long pendulum Choking up on a baseball bat Rotating your pencil Running with bent legs vs straight legs

Calculating Rotational Inertia The equation you use to calculate rotational inertia is different for different object rotating different ways. In general, rotation inertia is effected by the mass of the object and its lever arm/radius/distance from its rotational axis I=mr2 Rotational Inertia = mass of object x radius squared

Different Rotational Inertias for the Same Object Although one object will have the same mass at any time, you can change the axis that the object rotates on. This makes the object change its radius based on its rotational axis and changes the objects rotational inertia. Meter stick example

Three Different Rotational Axes Longitudinal Axis Medial Axis Transverse Axis Draw picture Pg. 217

Rotational Inertia and Rolling Which will roll down a hill faster a cylinder or a hallow cylinder with the same radius and mass? The object with its mass concentrated farthest from the center. The solid one will roll down faster Does the mass and the radius matter? - Objects of the same shape and mass but different sizes accelerate equally when rolled down an incline

Angular Momentum Momentum is how much and object resists changing its existing speed. Angular momentum is how much an object resists changing how fast it is rotating Angular Momentum = Iω Or Angular Momentum = Rotational Inertia x rotational velocity

Another Way to Calculate Angular Momentum Angular momentum = mvr Or Angular momentum = mass x velocity x radius Because of the angular momentum of spinning bike tires you can tilt a bike while moving forward but you can not when the wheels are not spinning

Conservation of Angular Momentum Angular momentum stays the same when no net external torque is acting on the object Iω=Iω Or Rotational inertia at the start x rotational velocity at the start = Rotational inertia at the end x rotational velocity at the end

Why a Figure Skater Spins Faster When They Pull Their Arms In When the skater has their arms out they have a large rotational inertia because rotational inertia is based on mass and radius but a slow rotational velocity When the skater has their arms in they angular momentum will not change but their rotational velocity will increase because their rotational inertia decreased because their radius is smaller

How to Simulate Gravity When an object is rotated it has centripetal force acting on it to allow the object to continue traveling in a curved path. The object also has a centrifugal force acting on it pushing outward. -If we spin any large object that contains people then the people will feel the centrifugal force pushing them to the outer edge of the object they are in. This feels like gravity to the people. http://www.youtube.com/watch?v=r0UUF0tYCJM