Angular velocity ----Even Table--->Linear velocity-----ZiTong Cheng

1.Determine the final angular velocity of the ring/disk/shaft/spool system for each case after the weight hits the ground. How is this angular 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

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

3.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?

4.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.

Because we are even table, so we do linear velocity.

Answer:
Based on the experimental data, the final linear velocity (V=2h/t) of the system directly reflects the motion of the falling weight. The small pulley (r=0.15cm) showed the highest measured linear velocity (0.218m/s), but due to its small radius causing significant sliding friction, the predicted value (0.101m/s) deviated by 53.7%. The medium (r=1.3cm) and large pulleys (r=2.5cm) had measured velocities of 0.299m/s and 0.487m/s respectively, with the large pulley's prediction (0.502m/s) showing only a 3.1% difference, validating the pure rolling assumption. Measurement errors primarily stemmed from timing accuracy (±0.1s) and non-ideal rolling with small radii, explaining the prediction failure for the small pulley. The results clearly demonstrate that linear velocity is inversely proportional to pulley radius, but the large-radius design (like the manufacturer's choice to wrap the cord around the ring) offers distinct advantages for motion stability - it avoids small-radius sliding issues while enabling controlled energy release through greater rotational inertia, which fundamentally explains why larger radii are preferred for starter cord attachment in practical applications.