Assignment of Angular Momentum Conservation

Assignment of Angular Momentum Conservation

Instructions  

Assignment of Angular Momentum Conservation

The conservation of angular momentum is the topic of this lab. In essence, we have a spinning disc with a certain amount of angular momentum: Li=IiiLi=Iii. Then we place a third disc on top of it. The internal force between the two discs does not cause any external torque. As a result, the two-disc system’s angular momentum is conserved: Lf=LiLf=Li, or

Ii?i=If?f

Ii?i=If?f

However, as the spinning system’s rotational inertia increases with the addition of the second disc, the angular speed decreases:

?f=(IiIf)?i The theory for this lab can be found in this manual: AK-RMV-conservation of angular momentum.pdf. Actions It’s worth noting that in the video above, it only covers the first part of the lab, when the two discs have the same mass. We expect the final angular speed to be half of the initial angular speed because the rotational inertia of a system of given shape is proportional to its mass, and the final mass is twice the initial mass: f=(IiIf)i=(mimf)i=12if=(IiIf)i=(mimf)i=12i

The conservation of angular momentum still applies to the theory of the second part of the lab (dropping the top disc onto a spinning washer of unknown mass): Iii=Iff

Iff=Iii=Iff

The rotational inertia of the washer with mass m1m1, inner radius r1r1, and outer radius R1R1 is IiIi, and you must calculate it using these parameters. If=Ii+12m2R22If=Ii+12m2R22, where m2m2and R2R2are the mass and radius of the top disc dropped onto the washer, respectively. Your task is to use the formulas above to calculate the washer’s mass, m1m1.

2. The Laboratory

To collect data, replay the video above.

Part 1: Placing a second disc of equal mass on top of the spinning base disc. Pausing the video at the following two points will reveal the initial and final values of the angular speed: before the top disc is dropped (see the PDF file here if the image below does not load properly: before collision.pdfActions): before collision and after the top disc is dropped and settles into the spin (see the PDF file here if the image below does not load properly: after collision.pdfActions): after collision
These two images were taken from a lab video. For each of the four trials —- 2A through 5A —- you must find the same two moments and record the initial and final angular speeds from the screen.

Part 2: dropping a disc onto an unknown mass spinning washer. For the remaining 5 trials in the video, repeat the data collection steps from part 1. (1B through 5B).
They provide some measurement results for the mass and size of each disc at the end of the video. This one is for the washer (if the image below does not load properly, see the PDF file here: dimension of the washer.pdfActions):
size of the washer
3. Laboratory Report

This is a quick lab report for a group. It should contain the following elements:

Equipment for the Coverpage (no serial numbers are needed). The equipment list can be found in the manual mentioned above.
See the table above for more information.
Write down the basic formulas for this lab, starting with the conservation of angular momentum. See the first paragraph for more information.
Part 1: Take the average value of the fifi ratio from the four trials’ data (2A through 5A). Determine the percent error —- 1/2 is the theoretical value.
Part Two: Write down the formulas, including the one for the washer’s rotational inertia (which you’ll need to find), which will lead to the final formula for the washer’s mass (m1m1). Plug in the angular speed values you got for each of the 5 trials (1B through 5B), and you’ll get 5 m1m1 values. As your final experimental value, take the average of these. After the lab reports are submitted, I will publish the m1m1 standard value. For maximum credit, your result should be within 10% of the published result.
Optional for this report unless part 1 contains a significant error (over 5 percent ).
Please save and upload the lab report as a Word or PDF document.

RUBRIC
Excellent Quality 95-100%	Introduction 45-41 points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.		Literature Support 91-84  points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.			Methodology 58-53 points Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.
Average Score 50-85%	40-38 points More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.		83-76  points Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.			52-49  points Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.
Poor Quality 0-45%	37-1 points The background and/or significance are missing. No search history information is provided.		75-1 points Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.			48-1 points There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met
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