### Torque and Moments of Inertia Pre-lab Assignment

This is the rotational equivalent of the "Motion with Constant Acceleration" experiment - review that before doing this one. In this experiment you will investigate moments of inertia by applying a torque to a disk that is free to rotate. The torque comes from a string wrapped around a pulley on the disk; the string passes over a second pulley and has a mass hanging from it.
We'll start by deriving equation (3) from the lab write-up. The simulation should be helpful.

Sketch a free-body diagram for the hanging mass m. The mass accelerates down when the system is released from rest. Apply Newton's Second Law to find the relationship between T, the tension, and a, the acceleration.

What is the connection between a, the angular acceleration of the disk, and a?

Show how combining your two equations above with equations (1) and (2) in the lab manual will give you equation (3) in the manual.

The tension is not the only force producing a torque. There is also a frictional torque present that opposes the disk's motion (this is minimized by supporting the disk on a cushion of air). Use the "Top View" of the experiment in the simulation to answer the following questions.

When the mass is falling, and the disk is speeding up, how does the direction of the frictional torque compare to the direction of the torque from the string?

 Same Direction Opposite Direction
When the mass is rising, and the disk is slowing down, how does the direction of the frictional torque compare to the direction of the torque from the string?
 Same Direction Opposite Direction
When is the magnitude of the disk's angular acceleration largest? When the disk is speeding up or when it's slowing down?
 Speeding up Slowing down Equal in both cases