Rotational Dynamics II

Rotational Dynamics II Physics Experiment 9 Lab Report Fall 2020 Purpose/Goal: The purpose of this lab is to examine the properties of rotational dynamics. The angular acceleration of a disk will be measured due to an applied torque, and the disk’s inertia will be calculated. The angular acceleration of a disk and a ring will then be measured, and their moment of inertia will be calculated. Finally, the angular momentum will be observed of the disk and ring both before and after a collision. Procedure Part A: 1) 2) 3) 4) 5) 6) 7) 8) Open the Excel Spreadsheet Exp9Data to input your subsequent data. Record the mass values of the ring and disk in Excel. Record the average mass of the ring and disk in the report. Record the diameter values of the disk in Excel. Record the average diameter of the disk in the report. Record the 3 values of the inside and outside diameter in Excel. Record the average diameter of the ring in the report. Calculate the theoretical values of the moments of inertia for both the disk and the disk and ring together. 9) Record the values for the diameter of the shaft of the rotating apparatus in Excel. 10) Record the average diameter of the shaft in the report. 11) Calculate the average radius of the shaft. 12) Record the values of Table 1 in the lab guide in Excel. 13) Record the average acceleration for each hanging mass in the report. 14) Using Excel, calculate a/(g-a) using the 4 average accelerations of the 4 hanging masses. 15) Plot the a/(g-a) values as a function of hanging mass. 16) Plot the trendline on the graph and find the slope of the graph. 17) Calculate the experimental moment of inertia using Equation 10 from last week’s experiment. 18) Compare the experimental and the calculated values of the moment of inertia for the disk and calculate their percent errors. 19) Record the values of Table 2 in the lab guide in Excel. 20) Calculate the experimental value of the moment of inertia for both the disk and ring. 21) Compare the experimental and theoretical values of the moment of inertia for the ring and the disk and calculate their percent errors. Procedure Part B: 1) Copy Table 3 into the lab report. 2) Determine the angular velocities right before and after the collision and record them in the report. 3) Use Equation 2 to calculate the angular momentum of the system before the collision. 4) Use Equation 3 to calculate the angular momentum of the system after the collision. 5) Compare the angular momentum of the system before and after the collision and calculate their percent differences. General Data: Part A Theoretical Calculations: Moment of Inertia for Disk: I = ½(mdisk) (D/2)2 I = ½(1.42077)(0.2275/2)2 I = 0.009192 kg*m2 Moment of Inertia for Disk and Ring System: I = ½(mdisk)(D/2)2 + (mring)(Davg/2)2 I = 0.009192 + (1.41872)( 0.11729/2)2 I = 0.01407 kg*m2 Part A Disk Data: Part A Disk Graph: The slope of this graph is 0.0251 kg-1. Part A Questions: 3) average mass of ring: 1418.72g = 1.41872 kg average mass of disk: 1420.77g = 1.42077 kg 5) average diameter of disk: 22.75 cm = 0.2275 m 7) average diameter of ring: 11.729 cm = 0.11729 m 10) average diameter of shaft: 3.02 cm = 0.0302 m 13) average acceleration for 50g: 0.010929 m/s2 average acceleration for 100g: 0.022989 m/s2 average acceleration for 150g: 0.035463 m/s2 average acceleration for 200g: 0.047605 m/s2 18)  The values of the experimental and theoretical moment of inertia for the disk are very similar; the experimental value has a percent error of only 1.22%. 21) The values of the experimental and theoretical moment of inertia for the disk and ring system are very similar; the experimental value has a percent error of only 1.21%. Part A Disk Results: Radius of Shaft: r = D/2 r = 0.0302/2 r = 0.0151 Experimental Value of Moment of Inertia of Disk: a/(g-a) = mr2/I = m(r2/I) (r2/I) = 0.0251 0.01512 = 0.0251*I I = 0.00908 kg*m2 percent error: % error: |experimental – theoretical | / theoretical = |0.00908 - 0.009192 | / 0.009192 % error: 1.22% Part A Disk and Ring Data: Part A Disk and Ring Graph: The slope of this graph is 0.0164 kg-1. Part A Disk and Ring Results Experimental Value of Moment of Inertia of Disk and Ring: a/(g-a) = mr2/I = m(r2/I) (r2/I) = 0.0164 0.01512 = 0.0164*I I = 0.01390 kg*m2 percent error: % error: |experimental – theoretical | / theoretical = |0.01390 - 0.01407 | / 0.01407 % error: 1.21% Part B Data: Part B Questions: 2) angular velocity right before collision: 22.12 rad/sec angular velocity right after collision: 15.03 rad/sec 5) The angular momentums before and after the system were very similar, and only had a 3.95% difference. Any type of difference between them implies that momentum wasn’t conserved, and this is likely due to an external net torque acting on the system. Part B Results: Initial Angular Momentum: Linitial = Idisk(wi) Linitial = 0.00908 (22.12) Linitial = 0.2008 kg*m2/s Final Angular Momentum: Lfinal = (Idisk + Iring)*(wf) Lfinal = (0.01390)*(15.03) Lfinal = 0.2089 kg*m2/s Percent Difference: % difference = |0.2008 – 0.2089| / [(0.2008 + 0.2089)/2] % difference = 3.95% Conclusion: The experimental values of the moments of inertia for the disk and the disk/ring system were found to be 0.00908 kg*m2 and 0.0139 kg*m2 respectively. The percent error of the experimental values of the disk and the disk/ring system were found to be 1.22% and 1.21%, respectively. The angular velocity before the collision was found to be 0.2008 kg*m2/s while the angular velocity after the collision was found to be 0.2089 kg*m2/s. Their percent difference was 3.95%. I can conclude that the experiment went very well, as the percent error for the experimental value of the moments of inertia for both systems were very small, and the percent difference for the angular velocities is very small, indicating that the objectives were clearly met, and the experiment was successful. Error Analysis: One source of error in this experiment would be systematic error, which would be introduced by the Capstone program which measured the disk’s and the ring/disk system’s accelerations. This program introduces its own error because such programs are often susceptible to bugs and other errors which skew the measurements. Also, triple beam balances, for example, can be seen as unreliable because they require more manual involvement than electronic balances. More manual involvement by humans naturally introduces more error.