Theory: That a relationship can be found be seen on a graph of acceleration vs. angular speed, to confirm Acceleration_centripetal=radius*angular speed^2 (a_c=r*w^2) .
Procedure: Using a heavy rotating disk, a timer, and logger pro; we measure the centripetal acceleration and time it takes to complete ten rotations, plugging in this data in a acceleration vs. angular spped^2 graph should give a relation that confirms our equation in the theory.
The Apparatus
*At 4.8 volts, the apparatus spun with an a_c of 1.908 m/s^2.
*The time for the first rotation was 0.7405 seconds, and 10 rotations had been completed in 17.234 seconds since the timer began.
*So subtracting the time for the first rotation from the end time is 16.4935 seconds to complete 10 rotations.
Results for all
|
4.8 volts
|
6.2 volts
|
7.8 volts
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8.8 volts
|
10.9 volts
|
12.6 volts
|
|
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before rotation (s)
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0.7405
|
0.2161
|
0.78729
|
0.12808
|
0.44378
|
0.07418
|
|
10th rotation (s)
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17.234
|
12.6919
|
9.02378
|
7.13992
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6.06639
|
4.64158
|
|
time for 10 rotations (s)
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16.4935
|
12.4758
|
8.23649
|
7.01184
|
5.62261
|
4.5674
|
|
acceleration m/s^2
|
1.908
|
3.573
|
7.891
|
11.13
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17.21
|
25.89
|
*angular speed (w) is calculated as 2Pi*number of rotations/time of rotations, so all we have to do to calculate w is multiply 2Pi by ten and divide by the total time for each ten rotations.
Graph
*Setting up an acceleration vs angular speed graph, we see a linear fit line works quite well.
*The slope is 0.1382, given that our model is a_c=r*w^2, 0.1382 must be the radius.
*The actual radius is 13.8 cm, which converts to 0.138, a near perfect prediction for our model.
Conclusion
*Our model was nearly perfect, accurately predicting the radius with the given data.
*I don't see any error with the concept of the experiment, or the equipment.
*The only uncertainty, perhaps, is with the actual measuring of the radius; as it the professor used
a meter stick an those can never be more accurate than +/-0.05.
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