Theoretical Modeling

Part 1: Rolling Cyclinder

The angular velocity of a rotating point charge can be described as:

and the angular velocity of a rotating object (larger than a point charge) can be described as:

Deliverable #1: Create an equation for angular velocity as a function of time for both of the scenarios above. Assume that the angle, mass, and radius are all constant.

Deliverable #2: Describe with words and/or equations how moments of inertia are calculated. Report the moment of inertia for the following objects: a hollow cyclinder rotating about its axis, a solid cyclinder rotating about its axis.

Part 2: Falling Rod

Deliverable #3: Using energy conservation determine the angular velocity of the rod right before it hits the ground, and the tangential speed of the center of mass and end of the rod right before it hits. This will require looking at a physics text or doing some good searching of the internet. Be sure to reference where you found your information, and if you found a solution online, verify it is correct by referencing the appropriate sections of a physics text.