The relationship between the rotational acceleration of a solid disk and the translational acceleration of a falling mass Abstract: We are creating an experiment to test how angular acceleration can be calculated. By using the appropriate tool we collect data about angular acceleration of a system and compare data we found to the theoretical value that we calculated. After that, we do an error analysis of the experiment and come up with a conclusion. Hypothesis: We should be able to calculate the value of angular acceleration by getting the data about our model.
Theory According to Newton’s second law:
F = m g – T = m a
after we put those equations together and then simplify it, we got :
Method
Equipments : 1 rotational apparatus* 1 mass hanger,50 g 1 rod clamp 1 string 1 meter stick 1 ruler 1 computer-based laboratory system 1 motion sensor 1 motion software 1 electronic balance
At first, we measure the radius of the bigger spool ,the smaller spool, and the disk. Secondly, we tie one side of string with the smaller spool and another side the 50g mass hanger. Thirdly, we put the motion sensor directly downward of the mass hanger. Then, we rotate the disk anti-clockwise to make the mass in a position where it is going to be dropped. Last ,we drop the mass hanger. We repeat this experiment 25 times and we collect the data every time. M disk 0.1067 r disk 0.045 I disk 0.0001
Mspool 0.01 R spool 0.025 I spool 3E-06
m 0.05 r spool 0.016
Anguler Aceleration Translational Acceleration
-59.38 -0.8596 -58.94 -0.9736 -59.16 -0.8354 -59.56 -0.7928 -59.5 -0.878 -58.56 -0.9088 -59.22 -0.9098 -59.1 -0.777 -59.24 -0.8812 -59.08 -0.8414 -59.34 -0.8428 -59 -0.8484 -58.88 -0.8694 -59.06 -0.8472 -59.06 -0.8332 -59.4 -0.898 -59.84 -0.847 -58.02 -0.9496 -60.3 -0.8084 -60.22 -0.8296 -59.48 -0.8018 -59.68 -0.903 -58.54 -0.8388 -59.96 -0.8484 -59.46 -0.8302
Theoretical Angular Acceleration 63.31138383 Theoretical Transitional Acceleration 1.012982141
Average Angular Acceleration -59.2792 Average Transitional Acceleration -0.858136
Stdv of Angular Acceleration 0.511679587 Stdv of Transitional Acceleration 0.046612828
Results and error analysis The experimental data in the table above shows that the theoretical value of angular acceleration (i.e. 63.31138383) does not lie in the range of average experimental angular acceleration ± standard deviation of angular acceleration (59.2792 ±0.511679587). This means that there has been a systematic error which is why there is a big variation. For the transitional motion, the theoretical acceleration (i.e. 1.012982141) was also not in the rage of the experimental transitional motion (i.e.0.858136±0.046612828) which also shows that there has been a systematic error. Even in this error the equation of the relation between the transitional acceleration and angular acceleration still hold authenticity. A=α R Where, A is the Transitional acceleration α is the angular acceleration R is radius
Conclusion There are errors due to which the theoretical value did not fall in the range of the experimental value. If this systematic error is removed then it is possible to achieve range which may include the theoretical value. Even so, the experimental averages are pretty close to the theoretical values, hence it can be said that our hypothesis and model was correct.