Theory: Part one that a change in mass of the pully, hanging or spinning disk, as well as the radius of the pulley will effect to angular acceleration. Part 2 the moment of inertia for the apparatus can be determined using the data collected in Part 1
Procedure: Determine the mass and radius' of the various disks and pulleys of the apparatus, get the apparatus to spin with both disks and just one, attach a pulley with a string to the apparatus and tie the other end to a known mass, allow the mass to "bob" up and down from the apparatus, and measure for angular acceleration. Compare results for Part 1 and calculate the moments of inertia for Part 2.
Apparatus
Measurements
*The radius and mass of the top steel disk, 6.323 cm and 1361 gams respectively.
*The radius and mass of the bottom steel disk, 6.332 cm and 1348 gams respectively.
*The radius and mass of the top aluminum disk, 6.330 cm and 466 gams respectively.
*The radius and mass of the small pulley, 2.5 cm and 10 gams respectively.
*The radius and mass of the large pulley, 5 cm and 37 gams respectively.
*The hanging mass 25 grams.
Acceleration Graph (lower)
Data
Expt #
|
grams hanging
|
Pulley
|
Disk
|
rad/s^2 down
|
rad/s^2 up
|
average rad/s^2
|
|
1
|
hanging mass
|
25
|
small
|
top steel
|
0.6026
|
-0.6522
|
0.6274
|
2
|
hanging mass*2
|
50
|
small
|
top steel
|
1.207
|
-1.311
|
1.259
|
3
|
hanging mass*3
|
75
|
small
|
top steel
|
1.758
|
-1.949
|
1.8535
|
4
|
hanging mass
|
25
|
large
|
top steel
|
1.161
|
-1.272
|
1.2165
|
5
|
hanging mass
|
25
|
large
|
top Al
|
3.293
|
-3.595
|
3.444
|
6
|
hanging mass
|
25
|
large
|
Top+ Bottom steel
|
0.5888
|
-0.6408
|
0.6148
|
Graph of Velocity of spinning disk and hanging mass
"Calculations" Part 1
*Since the pivot is at the center of mass of the apparatus and the acceleration is constant, we know angular acceleration= acceleration/radius of pulley, so the smaller the radius of the pulley the larger angular acceleration.
*Greater tension on the sting should equal a larger torque, and since torque= moment of inertia*angular acceleration, we should conclude that a greater hanging mass (therefore greater tension in the string) should cause higher torque value which would mean a higher angular acceleration.
*From the Velocity graph's we can determine the acceleration and angular acceleration from the falling mass and apparatus respectively from looking at the slopes.
*The acceleration of the mass is 0.02874 m/s^2, and the angular acceleration 0.6124 rad/s^2, while using the large pulley (0.05 m radius). So Angular acceleration equals acceleration divided by the radius(0.02874/0.05), and we get 0.5748 rad/s^2
Conclusion Part 1.
*The first "calculation" isn't confirmed from the data, when a trail was conducted using the same mass but different radius pulley, the greater radius produced a higher angular acceleration. This was not expected. I believe something must have gone wrong, but I don't know what.
*The second "calculation" was confirmed by the data, as a larger hanging mass did result in a greater angular acceleration.
*The final calculation was "close" to the actual measured angular acceleration, so that confirms the hanging mass' acceleration is the same to the tangential acceleration of the apparatus.
Calculation Part 2
*Sample
*Results
|
calculated from Data
|
|
0.004663131
|
|
0.004642941
|
|
0.004870745
|
|
0.005034936
|
|
0.001448455
|
|
-0.000735616
|
Conclusion Part 2
*My numbers were far off, I can only assume serious error occurred during measurements of the pulley's and disks, therefore none of my data is useful.
*Ideally the moment of inertia should have matched with the calculations, but they did not.
*Also my calculations didn't take into account friction in the system
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