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course Phy 201
Strap and magnetsUses metal strap, magnets, threaded rod with bolts and washers, die
Setup A: Using the TIMER, time the strap as it rotates to rest about the threaded rod, clicking with each 180 degree rotation. Click also when the strap comes to rest, and estimate how many degrees it has rotated since its last full 180 degree rotation.
Setup B: Repeat, but this time, with a ceramic magnet on each side of the axis of rotation, halfway between the axis and the end of the strap.
Setup C: Repeat once more but with the magnets positioned at the ends of the strap.
Setup D: Same as Setup A, except that the strap is taken off the threaded rod and placed on the die.
Setup E: Same as Setup A, except that the strap is taken off the threaded rod and placed on the die.
Setup F: Same as Setup A, except that the strap is taken off the threaded rod and placed on the die.
Report your data for Setup A (simply copy and paste from the TIMER output).
10.945
0.592
0.775
0.923
1.762
Appeared to be exactly 720 degrees
I can't tell what your 10.945 means.
You should also briefly explain what the numbers
0.592
0.775
0.923
1.762
mean, though I infer that these are time intervals for 180-degree intervals of rotation.
Rather than 'Appeared to be exactly 720 degrees', you should state something like 'total rotation 720 deg, +- 5 deg'. You decide how nearly exact your estimate was. Could be +- 10 deg, +- 2 deg, etc., but you should indicate the basis for your uncertainty estimate.
Similar comments could be made on your remaining data estimates. I can pretty much tell what you mean, but you should get in the habit of stating it.
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Report your data for Setup B.
8.303
0.788
1.095
2.534
Appeared to be exactly 540 degrees
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Report your data for Setup C.
5.052
0.762
1.047
1.281
1.699
3.731
Appeared to be exactly 900 degrees
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Report your data for Setup D.
451.683
2.246
1.373
About 30 degrees past 180.
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Report your data for Setup E.
18.111
1.046
1.435
1.638
2.636
2.481
About 45 degrees past 180.
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Your data appear to be good. See my notes on how it could have been reported more clearly, and apply those ideas in future reports. No problem for the moment.
Now your first data set is
0.592
0.775
0.923
1.762
This implies four time interval, the first running from clock time 0 to clock time 0.592 sec, the second from 0.592 sec to 0.592 sec + .775 sec = 1.57 sec, the third from 1.57 sec to 1.57 sec + 0.923 sec = 2.50 sec, and the fourth from 2.50 sec to 2.50 sec + 1.762 sec = 4.26 sec.
The midpoint clock time of your second interval is halfway between 0.592 sec and 1.57 sec, at about 1.08 sec.
You could easily calculate the midpoints of all four time intervals, and should do so.
Report your midpoints below:
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Each of your time intervals
0.592
0.775
0.923
1.762
corresponds to a 180 deg rotation. So for each interval you can easily find the average rate of change of angular position with respect to clock time. Find the average rates and report them below. Be sure to include a detailed calculation, with explanation, for one of your intervals.
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The moment of inertia of the strap itself is 1/12 M L^2, where M is its mass and L is its length. Assume the strap mass to be 70 grams.
The moment of inertia of a magnet attached to the strap is approximately M R^2, where M is the 50 gram mass of the magnet and R its distance from the axis of rotation (the axis of rotation is the threaded rod).
The total moment of inertia of the system is the sum of the moments of inertia of its components.
Find the moment of inertia for system A and report below:
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Report below a table of average rate of change of angular position vs. midpoint clock time, for the four intervals you observed for Setup A. Report also the moment of inertia:
Setup A
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You are going to make the same report for the remaining systems. You can save yourself some time by using your calculator or Excel to do the necessary calculations.
Find the moment of inertia for the system in Trial B, and show your calculation in detail:
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For each system report average rate of change of angular position vs. midpoint clock time, and also report the moment of inertia:
Setup B
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Setup C
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Setup D
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Setup E
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Note that average rate of change of angular position is also called angular velocity. So you have calculated a number of angular velocities.
Sketch a graph of angular velocity vs. midpoint clock time for each setup. Describe how well each graph can be 'fit' by a single straight line. In a good 'fit' the points will appear to be randomly scattered about the line.
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On the whole, does it seem plausible that for these systems, the angular velocity tends to decrease linearly with time?
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Good data. See my notes on how to improve data reporting in the future, then complete the analysis according to the appended notes.
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