Compare rolling theory to actual measurements

See the instructions for setting up this experiment to prepare for the race.

Roll the instructor's table away from the podium and place two wooden blocks under each of two legs, causing it to tilt at a gentle angle. Using masking tape, mark a "start" and "finish" line on the table. We'll call the length of this racetrack L, and the vertical rise from one end of the track to the other h. We'll measure these values in class and write them on the board.

1. What is the acceleration of an object which slides down the table without friction? Express this acceleration in two ways:
   • in terms of g, h, L
   • in cm per second squared, plugging in the actual measurements
2. How long should it take for an object to slide without friction down the table? Again, express this
   • in terms of g, h, L
   • in seconds, plugging in the actual measurements

We'll pause here to discuss your results.

There are five objects we will actually send down this table. They are:

• physics cart
• billiard cue ball (solid)
• racquet ball (hollow)
• black solid wooden disk
• big silver metal hoop

Use this worksheet (one per group) to record your answers to the following questions.

3. For each type of object,
   • write down the moment of inertia, in terms of M and R
   • solve for the final velocity v in terms of g, h
   • write down an expression for the linear acceleration of the object, in terms of g, h, L
   • solve for the time t it should take to reach the bottom, in terms of g, h, L
   • plug in values to find time t in seconds

4. rank the objects based on the time they should take to reach the bottom of the table: fastest is "number 1", next-fastest is "number 2", and so forth.

Near the end of the class period, we will actually send each object down the table and measure the time it takes to reach the bottom. You can then compare your predictions with the actual measurements.