1. 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

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

3. 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

4. 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

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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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.