# Angular Acceleration Worksheet - Excel

Document Sample

```					                                                     Pendulum

100

80

60

40

20
angle (degrees)

0
0   0.25   0.5   0.75   1    1.25       1.5      1.75   2   2.25   2.5   2.75
-20

-40

-60

-80

-100
time (sec)

Series1   Series2
pendulum
l=           1   m                 g=        9.8 m/s^2                torque = l*m*g*sin(q)
m=           0.5   kg
qo =          80   degrees assume initial velocity is zero             angular acceleration = torque/I
dt =        0.01   sec                                                 I = m*l^2
t            q            t        q''        q'               q=qo*cos(wt)         w=(g/l)^1/2
0          80    -4.82556 -9.65111            0                  80            zero order period: 2p(l/g)^0.5
0.01    79.97235    -4.82515 -9.65029 -0.09651                 79.9608            first order period: 2p(l/g)^0.5*(1+(si
0.02    79.88941    -4.82391 -9.64781 -0.19301                79.84325
0.03    79.75118    -4.82182 -9.64363 -0.28949                79.64746
0.04    79.55769    -4.81884 -9.63769 -0.38593                79.37362
0.05    79.30896    -4.81494 -9.62989 -0.48231                  79.022
0.06    79.00503    -4.81005 -9.62011     -0.5786             78.59294
0.07    78.64595      -4.8041 -9.60821 -0.67481               78.08687
0.08    78.23179       -4.797 -9.59401 -0.77089               77.50429
0.09    77.76262    -4.78866 -9.57732 -0.86683                76.84575
0.1    77.23853    -4.77896 -9.55792     -0.9626             76.11191
0.11    76.65962    -4.76778 -9.53556 -1.05818                75.30349
0.12      76.026    -4.75499 -9.50997 -1.15354                74.42127
0.13    75.33783    -4.74043 -9.48086 -1.24864                73.46613
0.14    74.59526    -4.72396 -9.44792 -1.34344                  72.439
0.15    73.79845      -4.7054  -9.4108 -1.43792               71.34088
0.16    72.94762    -4.68458 -9.36916 -1.53203                70.17286
0.17    72.04299    -4.66131 -9.32262 -1.62572                68.93607
0.18    71.08481      -4.6354 -9.27079 -1.71895               67.63173
0.19    70.07337    -4.60663 -9.21327 -1.81166                66.26111
0.2    69.00897    -4.57482 -9.14963 -1.90379                64.82557
0.21    67.89197    -4.53973 -9.07946 -1.99529                 63.3265
0.22    66.72274    -4.50115 -9.00231 -2.08608                61.76537
0.23    65.50171    -4.45887 -8.91774     -2.1761             60.14373
0.24    64.22935    -4.41265   -8.8253 -2.26528               58.46314
0.25    62.90616    -4.36228 -8.72456 -2.35353                56.72527
0.26    61.53269    -4.30753 -8.61507 -2.44078                54.93181
0.27    60.10954      -4.2482  -8.4964 -2.52693               53.08452
0.28    58.63738    -4.18406 -8.36812 -2.61189                51.18521
0.29     57.1169    -4.11492 -8.22984 -2.69558                49.23574
0.3    55.54887    -4.04058 -8.08116 -2.77787                47.23803
0.31    53.93411    -3.96087 -7.92173 -2.85869                45.19403
0.32    52.27351    -3.87561 -7.75121     -2.9379             43.10574
0.33    50.56801    -3.78465 -7.56931 -3.01541                40.97521
0.34    48.81862    -3.68788 -7.37576 -3.09111                38.80453
0.35    47.02641    -3.58517 -7.17034 -3.16487                36.59583
0.36    45.19253    -3.47644 -6.95289 -3.23657                34.35126
0.37     43.3182    -3.36164 -6.72328     -3.3061             32.07303
0.38    41.40468    -3.24073 -6.48145 -3.37333                29.76337
0.39    39.45333      -3.1137  -6.2274 -3.43815               27.42455
0.4    37.46558    -2.98059 -5.96119 -3.50042                25.05885
0.41    35.44291    -2.84147 -5.68293 -3.56003                 22.6686
0.42    33.38688    -2.69642 -5.39283 -3.61686                20.25613
0.43    31.29912    -2.54558 -5.09115 -3.67079                17.82382
0.44    29.18132    -2.38912 -4.77823     -3.7217             15.37404
0.45   27.03526    -2.22724    -4.45448   -3.76948    12.90919
0.46   24.86274    -2.06018    -4.12037   -3.81403    10.43169
0.47   22.66566    -1.88823    -3.77646   -3.85523    7.943974
0.48   20.44595    -1.71168    -3.42337      -3.893   5.448471
0.49   18.20562      -1.5309   -3.06179   -3.92723    2.947628
0.5   15.94671    -1.34624    -2.69248   -3.95785    0.443897
0.51   13.67132    -1.15812    -2.31624   -3.98477    -2.06027
0.52   11.38157    -0.96698    -1.93395   -4.00793    -4.56242
0.53   9.079652    -0.77326    -1.54651   -4.02727    -7.06009
0.54   6.767762    -0.57744    -1.15488   -4.04274    -9.55085
0.55   4.448133    -0.38003    -0.76005   -4.05429    -12.0322
0.56   2.123018    -0.18152    -0.36304   -4.06189    -14.5019
0.57   -0.20531    0.017559    0.035117   -4.06552    -16.9573
0.58   -2.53459     0.21669     0.43338   -4.06517      -19.396
0.59   -4.86252    0.415349    0.830697   -4.06083    -21.8158
0.6   -7.18683    0.613014    1.226029   -4.05253    -24.2142
0.61   -9.50524    0.809175    1.618349   -4.04027    -26.5889
0.62   -11.8155    1.003328    2.006656   -4.02408    -28.9375
0.63   -14.1154    1.194989    2.389979   -4.00402    -31.2577
0.64   -16.4027    1.383692    2.767384   -3.98012    -33.5474
0.65   -18.6752    1.568993    3.137985   -3.95244    -35.8041
0.66   -20.9308    1.750474    3.500949   -3.92106    -38.0258
0.67   -23.1674    1.927748    3.855496   -3.88605    -40.2102
0.68   -25.3829    2.100457    4.200913    -3.8475    -42.3552
0.69   -27.5753    2.268276    4.536551   -3.80549    -44.4587
0.7   -29.7427    2.430915    4.861831   -3.76012    -46.5186
0.71   -31.8831    2.588122    5.176244   -3.71151      -48.533
0.72   -33.9949    2.739678    5.479356   -3.65974    -50.4998
0.73     -36.076   2.885404    5.770808   -3.60495    -52.4171
0.74     -38.125   3.025155     6.05031   -3.54724      -54.283
0.75   -40.1401    3.158825    6.317649   -3.48674    -56.0958
0.76   -42.1197     3.28634     6.57268   -3.42356    -57.8535
0.77   -44.0625    3.407664    6.815329   -3.35784    -59.5546
0.78   -45.9668    3.522792    7.045584   -3.28968    -61.1974
0.79   -47.8315    3.631749    7.263499   -3.21923    -62.7801
0.8   -49.6552    3.734592    7.469184   -3.14659    -64.3013
0.81   -51.4366    3.831402    7.662805    -3.0719    -65.7596
0.82   -53.1748    3.922288    7.844576   -2.99527    -67.1534
0.83   -54.8685     4.00738    8.014759   -2.91683    -68.4813
0.84   -56.5167    4.086827    8.173654   -2.83668    -69.7422
0.85   -58.1186    4.160799    8.321599   -2.75494    -70.9348
0.86   -59.6732     4.22948     8.45896   -2.67173    -72.0578
0.87   -61.1798    4.293067    8.586134   -2.58714    -73.1102
0.88   -62.6375    4.351768    8.703537   -2.50127      -74.091
0.89   -64.0457       4.4058   8.811601   -2.41424    -74.9991
0.9   -65.4037    4.455387    8.910774   -2.32612    -75.8338
0.91     -66.711   4.500756    9.001511   -2.23702    -76.5942
0.92   -67.9669    4.542137    9.084274      -2.147   -77.2795
0.93     -69.171   4.579763    9.159525   -2.05616    -77.8891
0.94   -70.3228    4.613862    9.227725   -1.96456    -78.4223
0.95     -71.422   4.644664    9.289328   -1.87228    -78.8787
0.96   -72.4682    4.672392    9.344784   -1.77939    -79.2579
0.97   -73.4609    4.697264    9.394529    -1.68594    -79.5593
0.98       -74.4   4.719494    9.438989       -1.592   -79.7828
0.99   -75.2851    4.739286    9.478573    -1.49761    -79.9281
1    -76.116    4.756838    9.513675    -1.40282    -79.9951
1.01   -76.8925    4.772335    9.544671    -1.30769    -79.9837
1.02   -77.6144    4.785957    9.571914    -1.21224    -79.8939
1.03   -78.2815     4.79787     9.59574    -1.11652    -79.7258
1.04   -78.8938     4.80823    9.616461    -1.02056    -79.4796
1.05    -79.451    4.817182    9.634364      -0.9244   -79.1555
1.06    -79.953    4.824857    9.649715    -0.82805    -78.7539
1.07   -80.3998    4.831377    9.662753    -0.73156    -78.2751
1.08   -80.7913    4.836847    9.673695    -0.63493    -77.7195
1.09   -81.1273    4.841364    9.682727    -0.53819    -77.0878
1.1    -81.408    4.845007    9.690014    -0.44137    -76.3806
1.11   -81.6331    4.847846    9.695692    -0.34447    -75.5986
1.12   -81.8027    4.849935    9.699871    -0.24751    -74.7424
1.13   -81.9167    4.851316    9.702632    -0.15051     -73.813
1.14   -81.9751    4.852016    9.704033    -0.05348    -72.8113
1.15    -81.978     4.85205    9.704101    0.043557    -71.7382
1.16   -81.9252    4.851419    9.702837    0.140598    -70.5948
1.17   -81.8169    4.850108    9.700217    0.237626    -69.3823
1.18   -81.6529    4.848093    9.696186    0.334628    -68.1018
1.19   -81.4334    4.845332    9.690664     0.43159    -66.7545
1.2   -81.1584    4.841772    9.683545    0.528497    -65.3418
1.21   -80.8278    4.837347    9.674694    0.625332    -63.8651
1.22   -80.4418    4.831975     9.66395    0.722079    -62.3258
1.23   -80.0004    4.825563    9.651127    0.818719    -60.7254
1.24   -79.5037    4.818005    9.636011     0.91523    -59.0655
1.25   -78.9517    4.809182    9.618364     1.01159    -57.3478
1.26   -78.3445    4.798962    9.597923    1.107774    -55.5738
1.27   -77.6823       4.7872      9.5744   1.203753    -53.7454
1.28   -76.9652    4.773742    9.547484    1.299497    -51.8643
1.29   -76.1933     4.75842     9.51684    1.394972    -49.9324
1.3   -75.3668    4.741056    9.482113     1.49014    -47.9516
1.31   -74.4858    4.721463    9.442927    1.584961    -45.9238
1.32   -73.5506    4.699444    9.398887    1.679391     -43.851
1.33   -72.5615     4.67479    9.349581    1.773379    -41.7352
1.34   -71.5186     4.64729     9.29458    1.866875    -39.5785
1.35   -70.4224    4.616721    9.233443    1.959821     -37.383
1.36    -69.273    4.582858    9.165716    2.052155    -35.1509
1.37    -68.071    4.545469    9.090939    2.143813    -32.8844
1.38   -66.8166    4.504321    9.008641    2.234722    -30.5856
1.39   -65.5104    4.459177    8.918354    2.324808    -28.2568
1.4   -64.1528    4.409803    8.819606    2.413992    -25.9004
1.41   -62.7445    4.355965    8.711929    2.502188    -23.5186
1.42   -61.2858    4.297433    8.594865    2.589307    -21.1137
1.43   -59.7777    4.233983    8.467966    2.675256    -18.6882
1.44   -58.2206       4.1654   8.330799    2.759936    -16.2443
1.45   -56.6154    4.091477    8.182954    2.843244    -13.7845
1.46   -54.9629    4.012022    8.024043    2.925073    -11.3113
1.47    -53.264    3.926856    7.853711    3.005314    -8.82688
1.48   -51.5195    3.835818    7.671635    3.083851    -6.33385
1.49   -49.7306    3.738767    7.477534    3.160567   -3.83462
1.5   -47.8984    3.635585    7.271169    3.235342   -1.33164
1.51   -46.0238    3.526177    7.052353    3.308054   1.172656
1.52   -44.1082    3.410475    6.820951    3.378578   3.675799
1.53   -42.1529    3.288443    6.576887    3.446787   6.175341
1.54   -40.1592    3.160074    6.320148    3.512556   8.668831
1.55   -38.1285    3.025394    6.050788    3.575757   11.15383
1.56   -36.0624    2.884464    5.768929    3.636265   13.62789
1.57   -33.9625    2.737383    5.474766    3.693955    16.0886
1.58   -31.8303    2.584285     5.16857    3.748702   18.53355
1.59   -29.6677    2.425343    4.850686    3.800388   20.96033
1.6   -27.4763    2.260769    4.521538    3.848895   23.36658
1.61   -25.2581    2.090811    4.181623     3.89411   25.74993
1.62     -23.015   1.915758    3.831516    3.935926   28.10804
1.63   -20.7489    1.735933    3.471866    3.974242   30.43861
1.64   -18.4618    1.551696    3.103392     4.00896   32.73936
1.65     -16.156    1.36344    2.726879    4.039994   35.00802
1.66   -13.8334    1.171588    2.343176    4.067263   37.24237
1.67   -11.4963    0.976595    1.953189    4.090695   39.44024
1.68   -9.14694    0.778937    1.557875    4.110227   41.59945
1.69   -6.78749    0.579116    1.158233    4.125805    43.7179
1.7   -4.42026     0.37765       0.7553   4.137388   45.79351
1.71   -2.04754    0.175071    0.350141    4.144941   47.82425
1.72   0.328339    -0.02808    -0.05616    4.148442   49.80812
1.73   2.705063    -0.23125    -0.46251    4.147881   51.74318
1.74      5.0803     -0.4339   -0.86781    4.143256   53.62754
1.75   7.451727    -0.63548    -1.27097    4.134577   55.45935
1.76   9.817026    -0.83546    -1.67092    4.121868   57.23681
1.77    12.1739    -1.03331    -2.06662    4.105159   58.95819
1.78   14.52006    -1.22852    -2.45704    4.084492   60.62179
1.79   16.85327    -1.42062    -2.84123    4.059922   62.22599
1.8   19.17129    -1.60913    -3.21825     4.03151   63.76921
1.81   21.47196    -1.79362    -3.58725    3.999327   65.24994
1.82   23.75313      -1.9737     -3.9474   3.963455   66.66673
1.83   26.01272    -2.14899    -4.29799    3.923981   68.01819
1.84   28.24868    -2.31917    -4.63833    3.881001   69.30301
1.85   30.45904    -2.48392    -4.96784    3.834617   70.51991
1.86   32.64189    -2.64299    -5.28598    3.784939    71.6677
1.87   34.79536    -2.79617    -5.59234    3.732079   72.74527
1.88   36.91766    -2.94326    -5.88653    3.676156   73.75155
1.89   39.00708    -3.08414    -6.16828    3.617291   74.68557
1.9   41.06197    -3.21868    -6.43737    3.555608   75.54639
1.91   43.08074    -3.34684    -6.69367    3.491234   76.33319
1.92    45.0619    -3.46856    -6.93712    3.424297   77.04519
1.93      47.004   -3.58386    -7.16773    3.354926   77.68168
1.94    48.9057    -3.69278    -7.38556    3.283249   78.24206
1.95   50.76571    -3.79537    -7.59074    3.209393   78.72577
1.96   52.58281    -3.89174    -7.78347    3.133486   79.13233
1.97   54.35587    -3.98199    -7.96399    3.055651   79.46135
1.98   56.08381    -4.06629    -8.13257    2.976011    79.7125
1.99   57.76565    -4.14478    -8.28956    2.894686   79.88554
2   59.40043    -4.21765    -8.43531     2.81179    79.9803
2.01   60.98731   -4.28511   -8.57022   2.727437    79.99668
2.02   62.52546   -4.34736   -8.69471   2.641735    79.93467
2.03   64.01416   -4.40462   -8.80924   2.554788    79.79434
2.04   65.45271   -4.45713   -8.91426   2.466695    79.57581
2.05   66.84048   -4.50512   -9.01025   2.377553    79.27931
2.06   68.17691   -4.54884   -9.09769    2.28745    78.90511
2.07   69.46146   -4.58854   -9.17707   2.196473     78.4536
2.08   70.69366   -4.62444   -9.24889   2.104703    77.92521
2.09   71.87307   -4.65681   -9.31362   2.012214    77.32045
2.1    72.9993   -4.68587   -9.37175   1.919077    76.63993
2.11     74.072   -4.71187   -9.42375    1.82536    75.88431
2.12   75.09086   -4.73504   -9.47008   1.731122    75.05433
2.13   76.05559    -4.7556   -9.51119   1.636422     74.1508
2.14   76.96595   -4.77376   -9.54751    1.54131    73.17461
2.15    77.8217   -4.78973   -9.57946   1.445835    72.12671
2.16   78.62266   -4.80371   -9.60742    1.35004    71.00814
2.17   79.36865   -4.81589   -9.63178   1.253966    69.81998
2.18   80.05953   -4.82644   -9.65288   1.157648    68.56341
2.19   80.69516   -4.83553   -9.67105   1.061119    67.23965
2.2   81.27543    -4.8433    -9.6866   0.964409    65.84999
2.21   81.80025   -4.84991   -9.69981   0.867543    64.39582
2.22   82.26953   -4.85547   -9.71093   0.770545    62.87853
2.23    82.6832    -4.8601    -9.7202   0.673435    61.29964
2.24    83.0412    -4.8639   -9.72781   0.576233    59.66067
2.25   83.34349   -4.86697   -9.73394   0.478955    57.96324
2.26   83.59003   -4.86937   -9.73873   0.381616    56.20901
2.27   83.78078   -4.87116   -9.74232   0.284229     54.3997
2.28   83.91572    -4.8724    -9.7448   0.186805    52.53709
2.29   83.99483   -4.87311   -9.74622   0.089357    50.62299
2.3   84.01811   -4.87332   -9.74664     -0.0081   48.65929
2.31   83.98554   -4.87303   -9.74605   -0.10557     46.6479
2.32   83.89714   -4.87223   -9.74446   -0.20303     44.5908
2.33   83.75289    -4.8709    -9.7418   -0.30048    42.49001
2.34   83.55282   -4.86901   -9.73802   -0.39789    40.34758
2.35   83.29695   -4.86651   -9.73301   -0.49527    38.16561
2.36   82.98529   -4.86332   -9.72664     -0.5926   35.94624
2.37   82.61789   -4.85938   -9.71877   -0.68987    33.69165
2.38   82.19478    -4.8546   -9.70921   -0.78706    31.40405
2.39   81.71602   -4.84887   -9.69775   -0.88415    29.08567
2.4   81.18165   -4.84208   -9.68416   -0.98113    26.73878
2.41   80.59176   -4.83409   -9.66818   -1.07797     24.3657
2.42   79.94643   -4.82476   -9.64952   -1.17465    21.96874
2.43   79.24576   -4.81394   -9.62788   -1.27115    19.55025
2.44   78.48987   -4.80146   -9.60291   -1.36743    17.11261
2.45   77.67888   -4.78714   -9.57427   -1.46345     14.6582
2.46   76.81295   -4.77079   -9.54158     -1.5592   12.18942
2.47   75.89226   -4.75221   -9.50442   -1.65461    9.708695
2.48   74.91701   -4.73119   -9.46239   -1.74966    7.218458
2.49   73.88742   -4.70752   -9.41504   -1.84428    4.721148
cceleration = torque/I