Semester 1 Review Project:
Lab Goal: How does rotational inertia and angular momentum affect the speed of a skater while spinning?

Materials:

1.) Turn table
2.) Camera
3.) Logger-Pro
4.) Ice skates and ice skater
5.) 2 weights to hold while spinning

Procedure:

1.) Find the mass of each weight.
2.) Find the radius from your belly button to the weights in your arms outstretched, and then while your arms are in.
3.) Step on turn table while holding the weights.
4.) One partner videotapes from a birds eye view, while the other spins the person on the turn table.
5.) Give the spinner an initial velocity.
6.) The spinner begins with arms out and after two rotations pull arms in for another two rotations.



This is what a successful trial will look like. Nicole is holding 9 pound weights while she is spinning on the turn table. She spins twice with her arms out, and then twice with her arms pulled in. When her arms are fully extended she will rotate more slowly than she does when her arms are pulled in.

7.) After a successful trial upload the video to LoggerPro.
8.) Use LoggerPro to plot points throughout the video, following the person's shoulder during the entire rotation.
9.) Print out graph and find difference in time between each peak on graph. (The spaces inbetween peaks represents one rotation.)
10.) Using L=IW.pngfind the angular velocity of the spinner.

Procedure using L=IW.png:


physics_diagram_2.jpg
This diagram shows how the person's body is to be broken up.
The long cylinder represents the body while the squares on each side represent the weights being held in each hand.

1) Using this diagram, fill in the numbers in the equation:

equationasdf.png
i=m1r1^2.png is (the mass of one weight) x (the radius of one outstretched arm from the shoulder to the center of the weight being held in the hand) squared
m2_r2_..2.png is (the mass of the second weight) x (the radius of the other outstretched arm from the shoulder to the center of the weight being held in the other hand) squared

blah.png is 1/12th of (the mass of both arms combined) x (the length from finger tip to finger tip with arms outstretched) squared
*to find mass of single arm take 5.5% of body weight*
equation5.png is 1/2 of (the mass of the body without the mass of the arms and weights) x (the radius of one's stomach from side to belly button) squared

*You will need to complete two equations; one with data from when arms were out, and one with data from when arms were in*


2) Once the equation is set up, find omega.pnggraph.JPG

This is an example of what a graph from LoggerPro will look like. The peaks of this graph represent 1 rotation, so the area in between each peak is the spinner during a rotation.

Using this graph, find the time it took to complete one rotation with arms out, and another rotation with arms in. (You may need to refer back to the video to accurately determine when one rotation with arms out and in occurs).

Once the time it takes for spinner to complete one rotation with arms out and one rotation with arms in is found, divide one rotation, (360 degrees) by your time in seconds.
Your equation should be 360.png where t is the time it takes to complete one revolution with arms outstretched.

Using this same equation, solve for omega.png with arms in.

Refer back to the equation above.
After solving the equation fori.png with arms out, multiply that number by omega.png with arms out. Then multiply the number found for i.png with arms in by the number found for omega.pngwith arms in.

After multiply
i.png by omega.png for both arms in and arms out, compare your final two answers. If accurately done, the numbers should be the same.

Our Experiment

Using the same procedure listed above, we conducted the same experiment.

Data/Calculations:

Analysis of Graph:
graph.JPG
The four points noted in the graph represent two separate rotations.
From 4.7 to 6.7 seconds is one rotation with arms out, and from 6.83 to 8.0 seconds is one rotation with arms in.

  • This data shows that when the arms are brought in to the chest the person will spin at a greater speed.

Arms Out: 6.7s-4.7s=2.0 seconds
omega.png= 180
Arms In: 8.0s-6.83=1.17s
omega.png= 307.7
Arms Out: Radius= .804m
Arms In: Radius= .305m
Mass of weight: 4.08kg
Mass of single arm: 3.4kg
Length from finger tip to finger tip: 1.7m
Mass of body:
53.3kg

Our next step was to plug this data into the equation: equation.png

Arms outstretched:

equation6.png
equation3.png

Arms in:

equation-2.png
equation4.png
We then used the numbers we found for omega.png after using the equation 360.png, and used the equation equationsss.png

Arms outstretched:
equation10.png
equation-11.png

Arms in:
equation-111.png
equation112.png

*To prove that momentum is conserved, the solutions for L should ideally be identical. The ratio for L1 to L2 for our data is 14927.4/24000.6

Error analysis:
T
here are many ways in which mistakes could have been made during the experiment, which would lead to the final answers not equaling each other. One reason may be that the measurements taken were not exact. There may have been errors when the arm lengths were measured, when the mass of the weights were found, and when body weight was found. Many measurements were converted, and mathematical errors may have occurred during the conversions. Another possible error may have occurred while analyzing the graph and the video. If a dot was misplaced in LoggerPro or the graph was read incorrectly, it may have slightly altered the final answers. To find the mass of an arm, 5.5% of the spinner's body weight was found, which may not have
been exact because it is a general percentage rather than specific for the spinner's body. There may also have been an error in the construction of the equation. While many of the factors were accounted for, it is possible that while creating the equation not everything that affected the momentum was included. All of thes
e aspects of the calculations could have lead to the answers for the equations coming out wrong. These reasons could possibly be the reason that the two final answers do not equal each other when they should.

Conclusion:
This experiment attempted to prove that rotational inertia and angular momentum affect the velocity of a spin. Using the equation equationasdf.pngone is able to calculate the rotational inertia and the angular momentum. A video of a person on a turn table was uploaded in Logger-Pro, the graph that was produced from dot analysis, proved the initial theory that the more angular momentum the faster an object will spin. In the lad performed a major observation that was made was when the skater pulls there arms, alongwith weughts, into there chest while spinning they will begin spinning faster, therefore there angular momentum and rotational inertia are increasing. This lab application makes sense because of the real life tests performed. In the last two vidoes (below) of a skater spinning with three pound weights illustrates the initial lab question. It is apparent that when the arms are pulled tightly in the skater will spin faster. When the arms are pulled in the radius decreases so it is easier to spin faster.


These videos is are applications to real life from the experiment done in the classroom. One shows a skater jumping and spinning in the air. The other shows a spinner spinning and holding weights. This video shows that the same theory can be applied to a real life situation while a skater is spinning. It makes sense that momentum is conserved while spinning after viewing these videos, because it is apparent that while the skater is spinning slowly with her arms out, as soon as her arms are pulled in she speeds up.