Rotodyne

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Hofstra University *

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011B-A

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Physics

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Feb 20, 2024

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Hofstra University Physics department Student’s Name- Arpanpreet Kaur Grade- Experiment Title- Moment of Inertia “Rotodyne” Apparatus Experiment Number- 6 Date Performed- 11/15/2023 Labortaory Course - PHYS-011B Section- Laboratory Instructor- Professor Angela Lukaszewski Group Number- 3 Group Members- Arpanpreet Kaur
Abstract The objective of the lab is to simply show that the change in distribution of the mass, the moment of inertia changes. The equations that were used were a=2h/t^2, α=a/r, and T= m(g-a) r. The tools that were used were a meter stick, mass set, 4 additional masses, a stop pad and a digital timer. The theoretical values for all three investigations did not fall within our experimental range. Sketch of Apparatus
C harts and Graphs 2a. Moment of Inertia of the Wheel Alone M falling Average time to fall 1m Acceleration a=2h/T 2 Angular Acceleration α=a/r Applied Torque T=m(g-a)r kg sec m/s 2 [m/s 2 ]/m Nm 0.040 2.15413 0.4310 2.155 0.07503 0.060 1.75283 0.6509 3.2545 0.10990 0.080 1.524 0.8611 4.3055 0.14318 0.100 1.3715 1.0632 5.316 0.17493 0.120 1.27463 1.2310 6.155 0.20589 Least Square Fit X i Y i X i Y i X i 2 Y b = m b X i + b (Y b -Y i ) 2 2.155 0.07503 0.16168965 4.644025 0.074172 7.36164E-07 3.2545 0.10990 0.35766955 10.59177025 0.109795 1.1025E-08 4.3055 0.14318 0.61646149 18.53733025 0.143848 4.46224E-07 5.316 0.17493 0.92992788 28.259856 0.176588 2.74896E-06 6.155 0.20589 1.26725295 37.884025 0.203772 4.48592E-06 21.186 0.70893 3.33300152 99.9170065 8.4283E-06 Calculations
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2b. Moment of Inertia of Wheel plus 4 additional masses at the maximum allowable distance
M falling Average time to fall 1m Acceleration a=2h/T 2 Angular Acceleration α=a/r Applied Torque T=m(g-a)r kg sec m/s 2 [m/s 2 ]/m Nm 0.040 3.0364 0.216926 1.08463 0.076744 0.060 2.2426 0.397673 1.988365 0.112947 0.080 2.1347 0.438890 2.19445 0.149937 0.100 1.906 0.550534 2.75267 0.185189 0.120 1.7497 0.653285 3.266425 0.219761 Least Square Fit X i Y i X i Y i X i 2 Y b = m b X i + b (Y b -Y i ) 2 1.08463 0.076744 0.083238845 1.176422237 0.069520988 5.21719E-05 1.988365 0.112947 0.224579862 3.953595373 0.130613474 0.000312104 2.19445 0.149937 0.32902925 4.815610803 0.14454482 2.90756E-05 2.75267 0.185189 0.509764205 7.577192129 0.182280492 8.45942E-06 3.266425 0.219761 0.717832824 10.66953228 0.21701033 7.56619E-06 11.28654 0.744578 1.864444985 28.19235282 0.000409377 Calculations
2c. Moment of Inertia of wheel plus 4 additional masses at the minimum distance
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M falling Average time to fall 1m Acceleration a=2h/T 2 Angular Acceleration α=a/r Applied Torque T=m(g-a)r kg sec m/s 2 [m/s 2 ]/m Nm 0.040 2.9012 0.2376 1.188 0.07657 0.060 2.5173 0.3156 1.578 0.11393 0.080 2.0123 0.4939 2.4695 0.14905 0.100 1.7877 0.6258 3.129 0.18368 0.120 1.6095 0.7720 3.86 0.21691 Least Square Fit X i Y i X i Y i X i 2 Y b = m b X i + b (Y b -Y i ) 2 1.188 0.07657 0.09096516 1.411344 0.08487324 6.89438E-05 1.578 0.11393 0.17978154 2.490084 0.10446294 8.96252E-05 2.4695 0.14905 0.368078975 6.09843025 0.14924298 3.72413E-08 3.129 0.18368 0.57473472 9.790641 0.18236967 1.71696E-06 3.86 0.21691 0.8372726 14.8996 0.2190878 4.74281E-06 12.2245 0.74014 2.050832995 34.69009925 0.000165066 Calculations
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Discussions: For the first part of the experiment we start with plugging in the AC adapter to turn on the smart timer. The stop pad is placed directly below the rotodyne wheel. The rotodyne wheel has a radius of 0.2m. We hang different masses from the loop at the end of the string that is wrapped around the rotodyne wheel. The wheel lock is clicked on which causes the rotodyne wheel to not move and stay in one place. We are given the different masses that we are supposed to hang and a table is provided for us. We turn on the smart timer and we click select measurements until it shows the time option. Then we select the mode to two gates. We use a meter stick and we place it directly below the mass hanging. The meter stick would tell us the time it takes to fall 1m. If the mass is not directly below the meter stick, it is adjusted using the rotodyne wheel. The start button is clicked on the smart timer and the wheel lock is released. After the mass hanging hits the stop pad, the stop button on the smart timer is clicked and the time is recorded. The steps are repeated 2 times and the time was recorded. We found the average of the 3 times and then we wrote the values on the table. We found the acceleration using a=2h/t^2 then we wrote the values on our chart. We found the angular acceleration using the formula α=a/r, and we found the applied torque using the formula T= m(g-a) r. The theoretical moment of inertia of the wheel is given to us which is 0.0300 kg m^2. We made a least square fit analysis chart for y=mX+b where the x is the angular acceleration and the y is the applied torque. Our experimental value was 0.0324 kg/m^2. The uncertainty was ± 0.000526 kg/m^2. The theoretical value of moment of inertia does not fall within our experimental range of uncertainties. For the next part of the experiment we add 4 additional masses at the maximum distance on the rotodyne wheel. The rotodyne wheel has a radius of 0.2m. We were provided with the masses we had to hang. After we hang out mass , we use a meter stick and we place it directly below the hanging mass. The meter stick would tell us the time it takes to fall 1m. If the mass is not directly below the meter stick, it is adjusted using the rotodyne wheel. The start button is clicked on the smart timer and the wheel lock is released. After the mass hanging hits the stop pad, the stop button
on the smart timer is clicked and the time is recorded. The steps are repeated 2 times and the time was recorded. We found the average of the 3 times and then we wrote the values on the table. We found the acceleration using a=2h/t^2 then we wrote the values on our chart. We found the angular acceleration using the formula α=a/r, and we found the applied torque using the formula T= m(g-a) r. We then completed a least square fit chart for y=mx+b. The theoretical moment of inertia of the wheel is given to us which is 0.0300 kg m^2. We made a least square fit analysis chart for y=mX+b where the x is the angular acceleration and the y is the applied torque. Our experimental value was 0.0676 kg/m^2. The uncertainty was ± 0.0070887 kg/m^2. The theoretical value of moment of inertia did not fall within our experimental range of uncertainties. For the last part of the experiment we add 4 additional masses at the minimum distance on the rotodyne wheel. The rotodyne wheel has a radius of 0.2m. We were provided with the masses we had to hang. After we hang out mass , we use a meter stick and we place it directly below the hanging mass. The meter stick would tell us the time it takes to fall 1m. If the mass is not directly below the meter stick, it is adjusted using the rotodyne wheel. The start button is clicked on the smart timer and the wheel lock is released. After the mass hanging hits the stop pad, the stop button on the smart timer is clicked and the time is recorded. The steps are repeated 2 times and the time was recorded. We found the average of the 3 times and then we wrote the values on the table.We found the acceleration using a=2h/t^2 then we wrote the values on our chart. We found the angular acceleration using the formula α=a/r, and we found the applied torque using the formula T= m(g-a) r. We then completed a least square fit chart for y=mx+b. The theoretical moment of inertia of the wheel is given to us which is 0.0300 kg m^2. We made a least square fit analysis chart for y=mX+b where the x is the angular acceleration and the y is the applied torque. Our experimental value was 0.05023kg/m^2. The uncertainty was ± 0.003384kg/m^2. The theoretical value of moment of inertia did not fall within our experimental range of uncertainties. A graph is generated with (m(g-a)r vs α for each part of the experiment and all the experiment values are plotted on the same graph.
Honor Code: “I pledge on my honor that I have done this work with honesty and integrity, without giving or receiving unauthorized assistance.   I acknowledge that the use of all AI/ML automated tools are prohibited in this course.” SIGNATURE : Arpan
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