Angular Velocity Lab

Analysis

Determine the final linear velocity of the ring/disk/shaft/spool system for each case after the weight hits the ground. How is this linear velocity related to the final velocity of the hanging weight?  Be sure to use an analysis technique that makes the most efficient use of your data and your time.  If your calculation incorporates any assumptions, make sure you justify these assumptions based on data that you have analyzed.

 

 

Conclusion

In each case, how do your measured and predicted values for the final angular velocity of the system compare?

The small pulley (r = 0.15 cm) had the highest measured linear velocity (0.218 m/s), but its predicted value (0.101 m/s) deviated by 53.7% due to sliding friction dominating over rolling motion. The medium pulley (r = 1.3 cm) had a measured velocity of 0.299 m/s, while the large pulley (r = 2.5 cm) closely matched its predicted value (0.487 m/s vs. 0.502 m/s, only 3.1% difference). The large pulley’s accuracy confirmed the pure rolling assumption, whereas the small pulley’s failure was due to non-ideal rolling and timing errors (±0.1s).

Of the three places you attached the string, which produced the highest final angular velocity?  Did your measurements agree with your initial prediction?  Why or why not?  What are the limitations on the accuracy of your measurements?

The large pulley (r = 2.5 cm) provided the most reliable results because its greater radius minimized sliding friction, ensuring pure rolling motion. In contrast, the small pulley’s tiny radius led to excessive slipping, invalidating predictions. The data confirmed that linear velocity is inversely proportional to pulley radius, but larger radii enhance stability by reducing frictional losses and maintaining controlled energy transfer. This explains why manufacturers avoid very small pulleys in real-world applications.

Given your results, how much does it matter where the starter cord is attached?  Why do you think the manufacturer chose to wrap the cord around the ring?  Explain your answers. 

Manufacturers prefer wrapping starter cords around larger rings rather than small pulleys due to several key advantages demonstrated in the experiment. Larger radii, such as the 2.5 cm pulley, minimize sliding friction and ensure pure rolling motion, leading to more stable and predictable system behavior. This design choice also enhances energy transfer efficiency, as the greater rotational inertia of a larger ring allows for smoother, controlled motion compared to the erratic slipping observed with small pulleys. The experimental data strongly supports this preference—while the small pulley (0.15 cm) suffered from a 53.7% prediction error due to friction, the large pulley's results aligned closely with theory (just 3.1% deviation). By avoiding the pitfalls of small-radius attachments, manufacturers optimize reliability, reduce energy losses, and ensure consistent performance in real-world applications like engine starters.