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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 twodisc 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: AKRMVconservation 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.
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Assignment of Angular Momentum Conservation 