Lab 4/17 Angular Velocity

 

 Lab 4/17: Angular Velocity

Purpose

The purpose of this assignment was to experimentally determine angular velocity of the system and compare it to the theoretical value

Procedure

A string was wrapped around a ring with a mass attached to the other end of the string. As an odd table group, the mass was dropped while the amount of revolutions were counted to determine the angular velocity. This procedure was repeated with 2 additional rings at different sizes. 

Results

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.

The relationship between final velocity of the hanging weight and the angular velocity is described through the model v=rw. Based on the experimental heights and radius measured, the angular velocity was calculated to determine the accuracy of the observed angular velocity. It was determined that both angular velocities were somewhat similar in result. 

Conclusion

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

In each case, our measured angular velocities ended up being a bit lower than the values we had predicted. This makes sense when you consider that our calculations didn’t account for things like friction in the axle or any air resistance. Plus, there could’ve been a little slippage with the string as it unwound, which would cause the system to lose some energy and not spin as fast as expected.

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?

Out of the three string attachment points, the medium ring gave us the highest angular velocity at 5.40𝜋 rad/s. This result was surprising because we originally thought the smallest ring would spin the fastest. Our reasoning was that a smaller radius should lead to a higher angular velocity, since there's less rotational inertia to overcome. But our data didn’t match that prediction. One possible reason for that difference could be slippage between the string and the surface of the ring, which would definitely affect how much rotational energy was transferred. Other factors like uneven mass distribution or friction in the setup could’ve played a role too.

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.

From what we saw, the place where the string is attached does matter. The radius of attachment affects how much torque gets applied to the system. A bigger radius can create more torque, which helps the system spin up faster—but it also increases the moment of inertia, which resists that motion. So there's a bit of a trade-off. It makes sense that the manufacturer chose to wrap the starter cord around the ring—it's probably a good balance between creating enough torque and keeping slippage to a minimum. Plus, the ring likely provides a smoother and more consistent surface for the string to grip.