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Data Spreadsheets


First the main stick was attached to a horizontal wheel. Using a weight attached to a string wrapped around the wheel and computer data collection, a graph was made of angular v vs. t. The slope of this graph was 55.318, or a. The torque applied was the added mass (.075 kg) * gravitational constant (9.8 m/s^2) * radius (.0265 m), or .019478. To find I, this was divided by acceleration. The I found was .020184.

Using the following formulas each column was calculated from the gathered x and y positions of the center of mass (CM), end of stick, and contact point. The I found above was also used.


 
angle = arcsin(x.end-x.cm)/half length w = change in angle / change in time
alpha = change in w / change in t F = torque / distance from contact point to CM
Torque = (alpha.last+alpha.this+alpha.next)/3 * I
a.x = F * cos(angle) / m a.y = - F * sin(angle)/m - g

In the data tables below, notice the change in sign of the acceleration in the x-direction between each instance of contact. The magnitude of the y-acceleration, on the other hand, gets close to zero and then increases.

Data without Foil


 
CM
CM
End
End
Contact
Contact
angle
w
alpha
Torque
F
a (x)
a (y)
v (x)
v (y)
a (x)
a (y)
time
x
y
x
y
x
y
from vert
predict
predict
measure
measure
measure
[s]
[m]
[m]
[m]
[m]
[m]
[m]
(rad)
(rad/s)
0.77
0.68
0.359
0.87
0.47
0.7824
0.4139
0.8809
1.149
1.5
0.003
0.02
0.047
-9.86
0.88979
0.46837
0.8
0.69
0.346
0.89
0.43
0.79
0.3912
0.9179
1.112
-1.11
-0.07
-0.54
-1.22
-8.21
0.22823
-0.3994
-0.8629
-1.1318
0.83
0.69
0.346
0.89
0.41
0.7919
0.3799
0.9429
0.751
-10.8
-0.31
-2.4
-5.19
-2.65
0.05706
0
-5.1403
11.994
0.87
0.69
0.35
0.89
0.41
0.79
0.378
0.93
-0.39
-34.1
-0.373
-2.89
-6.36
-1.27
-0.0569
0.11377
-3.4217
3.41659
0.9
0.69
0.359
0.88
0.41
0.7862
0.3836
0.9054
-0.74
-10.5
-0.226
-1.75
-3.98
-4.73
-0.0571
0.28529
-0.0051
5.13511
0.93
0.68
0.367
0.88
0.42
0.7786
0.3969
0.8931
-0.37
11.1
-0.071
-0.55
-1.27
-8.22
-0.1141
0.22523
-1.7134
-1.8036
0.97
0.68
0.378
0.87
0.44
0.7786
0.412
0.8683
-0.74
-11.1
0.011
0.085
0.202
-10
-0.1108
0.34132
0.1002
3.48625
1
0.68
0.393
0.86
0.47
0.7635
0.4309
0.8455
-0.69
1.67
-0.134
-1.04
-2.54
-6.94
-0.1141
0.45345
-0.0999
3.35737
1.03
0.67
0.408
0.85
0.5
0.7578
0.4555
0.8114
-1.03
-10.5
-0.465
-3.6
-9.13
-0.19
-0.1727
0.45758
-1.7602
0.12379
1.07
0.67
0.423
0.83
0.54
0.7408
0.48
0.7067
-3.08
-60.2
-0.331
-2.57
-7.18
-3.67
-0.1676
0.44412
0.1539
-0.4078
1.1
0.66
0.44
0.8
0.59
0.7257
0.5159
0.6284
-2.37
21.5
-0.26
-2.02
-6.01
-5.43
-0.2848
0.51515
-3.4471
2.08923
1.4
0.52
0.395
0.33
0.55
0.4139
0.4781
-0.8924
-0.64
-0.46
-0.7
-5.43
-12.5
-25.3
0.36986
0.28214
1.43
0.51
0.376
0.3
0.5
0.395
0.4403
-1.0262
-4.06
-104
-0.354
-2.75
-5.23
-18.4
-0.2273
-0.5727
-0.4265
-0.6106
1.47
0.5
0.357
0.28
0.46
0.378
0.4139
-1.1047
-2.31
51.4
0.012
0.094
0.155
-9.49
-0.3353
-0.5559
-3.2734
0.51045
1.5
0.49
0.346
0.27
0.44
0.3704
0.3931
-1.1221
-0.53
54
0.816
6.33
10.1
11.17
-0.1697
-0.3455
4.8705
6.18905
1.53
0.49
0.336
0.26
0.42
0.3666
0.3818
-1.1221
7E-15
16
0.67
5.192
8.283
7.404
-0.1727
-0.2848
-0.0918
1.83655
1.57
0.49
0.331
0.27
0.42
0.361
0.3761
-1.0879
1.005
29.6
0.395
3.06
5.226
0.167
-0.0559
-0.1676
3.5408
3.55156
1.6
0.48
0.327
0.27
0.42
0.3629
0.378
-1.0404
1.438
13.1
0.596
4.624
8.602
4.869
-0.0576
-0.1152
-0.0498
1.54399
1.63
0.48
0.323
0.28
0.43
0.3685
0.3818
-0.9429
2.954
45.9
0.312
2.421
5.231
-2.59
0
-0.1121
1.7447
0.09183
1.67
0.49
0.323
0.3
0.44
0.3761
0.3931
-0.8571
2.524
-12.6
0.516
4.004
9.641
1.333
0.05588
0
1.6934
3.39761
1.7
0.49
0.327
0.33
0.46
0.3912
0.4063
-0.7265
3.959
43.5
0.404
3.135
8.618
-2.14
0.11515
0.11212
1.7432
3.29768
1.73
0.5
0.329
0.36
0.49
0.4177
0.4252
-0.564
4.925
29.3
0.517
4.01
12.46
-1.92
0.22727
0.05758
3.3976
-1.6529
1.77
0.51
0.333
0.42
0.52
0.4555
0.4441
-0.3918
5.065
4.13
0.569
4.412
15
-3.6
0.39118
0.11176
4.9668
1.64209
1.8
0.53
0.34
0.49
0.55
-0.1689
6.754
51.2
0.372
2.885
10.46
-8.02
0.57273
0.2303
5.3397
3.48642

Data with Foil


 
CM
CM
End
End
Contact
Contact
w
alpha
Torque
F
a (x)
a (y)
v (x)
v (y)
a (x)
a (y)
time
x
y
x
y
x
y
predicted
predicted
measured
measured
measured
[s]
[m]
[m]
[m]
[m]
[m]
[m]
(rad/s)
0.47
0.85
0.616
1.02
0.74
0.8963
0.6466
0.7533
0.5
0.86
0.577
1.06
0.67
0.9546
0.6216
0.9186
4.964
0.16817
-1.1682
0.53
0.87
0.547
1.07
0.6
0.9518
0.5689
0.9199
0.04
-148
0.41441
-0.9159
0.57
0.88
0.522
1.08
0.55
0.9796
0.5384
0.9361
0.484
13.3
-0.877
-6.8
-14.8
10.35
0.16766
-0.7485
-7.4099
5.02742
0.6
0.88
0.508
1.08
0.52
0.9768
0.5189
0.9568
0.623
4.16
0.104
0.805
1.705
-12.2
0
-0.4174
-5.0199
9.91274
0.63
0.87
0.508
1.08
0.52
0.9685
0.5162
0.9753
0.555
-2.04
-0.555
-4.3
-8.87
3.294
-0.1682
0
-5.0501
12.5351
0.67
0.89
0.516
1.08
0.54
0.9768