The decelerating wheel experiment -- analysis

If one spins a wheel rapidly and holds it in mid-air, it will continue to spin for quite a while. However, the combination of air resistance and friction will combine to slow the wheel's rotation. Over the course of several minutes, the wheel's angular speed will gradually decrease, and, eventually, it will stop.

I performed this experiment: after spinning the wheel rapidly, I measured its angular speed many times over the next few minutes. My measurements are shown below:

  time           angular speed
  (sec)            (rad/sec)
----------------------------------
   15               14.7
   30               12.6
   45               10.7

   60                9.2
   75                8.10
   90                6.57
 
  105                5.50
  120                4.47
  135                3.35
----------------------------------
 

You can look at a graph of this information (or a smaller version if necessary).

1. Estimate the average angular acceleration using the first three measurements.
2. Estimate the average angular acceleration using the last three measurements.
3. Did the wheel decelerate at a constant rate? Explain.
4. What was the angular displacement of the wheel between 15 and 30 seconds?
5. What was the angular displacement of the wheel between 120 and 135 seconds?
6. Estimate the total angular displacement of the wheel from start (0 seconds) to finish (135 seconds).
7. Pretend that during this experiment, the wheel had not been spinning horizontally, but was rolling down the hallway outside the classroom. Would it have reached the far end of the hallway before stopping?

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.