Angular Velocity Lab

 

How is angular velocity related to the final velocity of the hanging weight?

Angular velocity is related to the linear velocity of the hanging mass by v=rω, where r is the radius of the spool. Rearranging gives ω=rv​. This relationship is also used in energy equations to solve for final velocity.

How do your measured and calculated values for angular velocity compare?

All measured values are less than predicted values. This is understandable since predicted values are calculated using ideal situations and do not include nonconservative forces like friction. To within 20%, on average, measured values are close to predicted values, with the difference due to energy loss in the system.

Of the three attachment points, which had the highest final angular velocity? Did your measurements agree with your prediction? Why or why not? What are the limitations of your measurements?

The big spool had the largest final angular velocity, as predicted. This result is consistent with the results from other groups, where angular velocity was calculated using the work-energy equation by plugging in v=rω. However, the constraints include measurement error, inaccuracy in timing, and the lack of provision for nonconservative forces like friction, which may depend on the accuracy of the results.

Time measurements and disregard of work done by nonconservative forces are the greatest drawbacks of the present experimental arrangement. Human response time in recording the mass dropping from a height to the ground gives a large uncertainty and is expected that the recorded time is larger by default. An example of an energy loss that was left out would be the bearing system that allows the spool to turn. Within that, there is an inherent frictional component that would impact the system's energy in a non-trivial manner. Similarly, real-world conditions would imply that there is rope slippage to some degree, so one can reasonably assume that energy is lost there as well.

On the basis of your results, how important is the location where the starter cord is wound? Why do you think the manufacturer wound the cord around the ring? Describe your answers.

It makes a significant difference where the starter cord is wound on the basis that data gathered depicts differences in angular velocity using different size spools.    Depending on the application, a producer would have to compromise between usability for the user and desired power to be transferred. The above measurements indicate that a ring would have a smaller moment of inertia, hence making a pull effortless on a user and transferring the most direct pull-energy power. A producer may also manipulate the ratio of pull to power and rotations of the attached system (i.e. crankshaft) by changing the radius to achieve a desired outcome.