This lab is about the conservation of angular momentum. Basically, we have a disc spinning with a certain amount of angular momentum: Li=Ii?iLi=Ii?i. We then drop another disc on top of it. The force between the two discs is internal, and does not cause any external torque. As a result, the angular momentum of the two-disc system is conserved: Lf=LiLf=Li, or

Ii?i=If?fIi?i=If?f

However, since the rotational inertia of the spinning system increases with the addition of the 2nd disc, the angular speed decreases:

?f=(IiIf)?i<?i?f=(IiIf)?i<?i

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**1. Pre-lab Activities**

- Watch this video for the lab. It has the equipment, procedures, and the data you need. It actually contains two separate parts: dropping a top disc with the same mass as the base disc, and dropping a top disc onto a washer of unknown mass.Link (Links to an external site.)
- Read this manual for the theory of this lab: AK-RMV-conservation_of_angular_momentum.pdf ActionsNote that it only covers the first part of the lab in the video above, when the two discs have the same mass. Since the rotational inertia of a system of given shape is proportional to its mass, and the final mass is twice the initial mass, we expect the final angular speed to be half of the initial angular speed:

?f=(IiIf)?i=(mimf)?i=12?i?f=(IiIf)?i=(mimf)?i=12?i .

- For the theory of the 2nd part of the lab (dropping the top disc onto a spinning washer of unknown mass), the conservation of angular momentum still applies:

Ii?i=If?fIi?i=If?f .

Here IiIi is the rotational inertia of the washer of mass m1m1, inner radius r1r1, and outer radius R1R1— you need to figure out the formula for IiIibased on these parameters. The final rotational inertia is If=Ii+12m2R22If=Ii+12m2R22 , where m2m2and R2R2are the mass and radius of the top disc dropped onto the washer. Your job is to find the mass m1m1of the washer from the formulas above.

**2. The Lab**

Launch the video above again to collect data.

**Part 1**: Dropping a second disc of the same mass onto the spinning base disc. You can find the initial and final values of the angular speed by pausing the video at the following two moments —- before the top disc is dropped (see the PDF file here if the picture below does not load properly: before collision.pdfActions): and after the top disc is dropped and settles into the spin (see the PDF file here if the picture below does not load properly: after collision.pdfActions):

These two pictures came from the lab video. You need to find the same two moments for each of the 4 trials — 2A through 5A — and record the initial and final angular speeds from the screen.

**Part 2**: dropping a disc onto the spinning washer of unknown mass. Perform the same data collection steps as part 1, for the remaining 5 trials in the video (1B through 5B).- At the end of the video they provide some measurement results for the mass and size of each disc. This one is for the washer (see the PDF file here if the picture below does not load properly: dimension of the washer.pdfActions):

**3. The Lab Report **

This is a **short, group lab report**. It should include the following parts:

**Coverpage****Equipment**(no serial numbers are needed). See the manual above for the equipment list.**Data**: See above.**Analysis**: First, write down the basic formulas for this lab: the conservation of angular momentum. See the first paragraph above.**Part 1**: Take the average value of the ratio of ?f?i?f?ifrom the data of the four trials (2A through 5A). Find the percent error — the theoretical value is 1/2.**Part 2**: Write down the formulas, including the one for the rotational inertia of the washer (which toy need to find), leading to the final formula for the mass of the washer (m1m1). Plug in the values of the angular speeds you obtained for each of the 5 trials (1B through 5B), and obtain 5 values of m1m1 Take the average of these as your final experimental value. I will publish the standard value of m1m1after the lab reports are submitted. Your result should be within 10% of the published result for maximum credit.

**Discussion:**Optional for this report unless part 1 has a large error (over 5%).

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