LAB10 - This lab is one of the weekly labs that you must complete. PDF

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This lab is one of the weekly labs that you must complete....

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PHYS 172

LAB 10 ANGULAR MOMENTUM PRINCIPLE : Finding Moment of Inertia

SPRING 2021

LAST NAME (ALL CAPS): ANNEPU_____________ FIRST NAME (ALL CAPS) SRIKEERTHAN_________________ PUID:32511138______ LAB Section DAY FRIDAY_____ LAB Section TIME 7:30-9:20______ LAB GROUP#12___ (Asynchronous Students: for DAY and TIME, please type DIST)

Learning Goals After completing this activity, you should be able to: ● Use the angular momentum principle to find the moment of inertia of an object.

Equipment Needed One iOLab kit, masking tape (2 identical rolls – new/unused), ruler, one or multiple books, clipboard or plank, string, ruler.

Procedure Q01: Take the new/unused masking tape roll and calculate its mass using the iOLab kit. Show your set up and calculations clearly. Hint: Suspend the masking tape roll from the Force sensor and measure the 'Force' using the IOLab sensor. From the 'Force,' determine the mass of the masking tape roll. Fg = mg Fg = 0.896 0.896 = mg 0.896/9.8 = m m = 0.0914 TAKE A PHOTOGRAPH OF THE SET UP YOU USED TO FIND THE MASKING TAPE ROLL MASS. PASTE IT BELOW

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TAKE A SCREENSHOT OF THE iOLab FORCE GRAPH YOU GOT TO FIND THE MASS OF THE MASKING TAPE ROLL. PASTE IT BELOW

SHARE YOUR DATA WITH YOUR GROUP MEMBERS Please note that the TAG NAME for your shared data is in this format: 'LAB GROUP'(as given in the "L-000_00" format) + ' LAB #' (e.g. "LAB10" for this week) E.g. if you are in Lab section L-052 and Group 7, the TAG NAME for ALL data that you share for this lab will be L-052_07+LAB10 [For those students who do not have the iOLab kit because you are outside the U.S./Canada, your Lab Grader GTA will share data with you. But you do NOT need to share it with your Group.] SEE LAB Data Sharing Instructions provided on Brightspace. Go to Content (top menu) > LAB Data Sharing (side bar)

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Building a composite object Take the two new/unused rolls of masking tape and using some other masking tape (or another stronger tape, e.g., duct tape) attach them to the two ends of the iOLab cart to create a composite object. The composite object looks like the figures below.

With your group share your ideas with your team regarding the slope of the ramp you will use during the experiment before collecting data. Come to a consensus about what angle you will use such that you can share your results. Use the stack of books (or a single book) and the clipboard (or a plank) to create a set up shown below and place the composite object (iOLab + two masking tape rolls) at the top of the ramp and let go. This is just a practice to get a feel for the system and make sure the composite object rolls down the ramp (clipboard/plank) without slipping. TAKE A PHOTOGRAPH OF THE SET UP AND PASTE IT BELOW [YOU MAY NEED HELP TO TAKE THE PHOTO]

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Q02: How does the angle of incline affect (a) the torque (relative to the Y-axis of the iOLab kit) acting on the system? (b) your final answer for the moment of inertia of the composite object? (a) The angle of incline affects the magnitude of the torque acting on the system, and directing a perpendicular force increases the torque. (b) The greater the incline, the greater the velocity, which in turn results in a greater moment of inertia.

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After you have tested the set up, you are now ready to start data collection Place the composite object (iOLab + tapes) on a flat horizontal surface so that it does not roll. Examine the three axes marked on the iOLab and also think about how the composite object will rotate. Then decide which one of the three axes x, y, or z, is important in this experiment, i.e., about which axis will the composite object rotate. Q03: Which one of the three axes is relevant to the rotation of the iOLab? Explain why this is so. An angular velocity that points along the positive y-axis therefore corresponds to a counterclockwise rotation, whereas an angular velocity that points along the negative y-axis corresponds to a clockwise rotation. So, the y- axis is relevant to the rotation of the iOLab because of its correlation to angular velocity. Also, as we can see from the graph below, the only axis that really experiences change is the y-axis.

Turn on the iOLab cart and start the iOLab application on your computer, with the Bluetooth USB plugged in. Select 'Gyroscope'. Three graphs for the angular velocity of rotation about each of the three axes x, y, and z appear. We are interested in the angular velocity about only one of these axes (see Q03). Un-select the other axes. With the iOLab application running, gently place the composite object at the top of the ramp (as shown in the figure above) and let go. The graph should show the change in the angular velocity of the composite object as it rolls down the incline. Highlight the portion of the graph that corresponds to the duration when the composite object was rolling down the incline. TAKE A SCREENSHOT OF THE iOLab GRAPHS (WITH THE HIGHLIGHTED PORTION). PASTE IT BELOW

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SHARE YOUR DATA WITH YOUR GROUP MEMBERS Please note that the TAG NAME for your shared data is in this format: 'LAB GROUP'(as given in the "L-000_00" format) + ' LAB #' (e.g. "LAB10" for this week) E.g. if you are in Lab section L-052 and Group 7, the TAG NAME for ALL data that you share for this lab will be L-052_07+LAB10 [For those students who do not have the iOLab kit because you are outside the U.S./Canada, your Lab Grader GTA will share data with you. But you do NOT need to share it with your Group.] SEE LAB Data Sharing Instructions provided on Brightspace. Go to Content (top menu) > LAB Data Sharing (side bar)

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Q04: From the graph above, determine the angular acceleration of the composite object as it rolled down the incline? Show your calculations clearly . Hint: You will need to use the initial and final angular velocity and the time duration.

a = 31.7368 rad/s^2

The next two questions will allow you to determine the mass of the composite object Q05: In previous labs, you found the mass of the iOLab Cart, write up that value again below (If you want you can calculate it again using the iOLab kit) Page 9 of 17

m = 0.17112 kg Q06: What is the mass of the composite object (iOLab Cart + 2 masking tapes)? Show you calculations clearly Hint: You may need to refer to your answer to Q01 and Q05 above. Mass of 1 tape roll: m = 0.0914 kg Mass of iOLab cart: m = 0.17112 kg Mass of composite object: (2 * 0.0914 kg) + 0.17112 kg = 0.35392 kg

The next four questions will help you find the torque acting on the composite object as it rolls down the inclined plane. Q07: What is the angle of incline that the composite object rolls down? Show your calculations clearly. Hint: Measure the length and the height of the incline using the ruler. Then, find the angle from there.

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angle = 36.0617 degrees Q08: What is the force component acting on the composite object down the inclined plane? Show your calculations clearly. Hint: Use the answers to the previous questions and the value of the acceleration due to gravity. The only force acting on the system is gravity, therefore the only force component will be -mg. F = 0.35392 kg * (-9.8 m/s) = -3.468416 N Q09: What is the radius of rotation of the composite object? Hint: Measure the diameter of the tape and find its radius. d = 0.118 m r = d/2 r = 0.059 m Page 11 of 17

Q10: What is the torque acting on the composite object due to the force acting down the ramp? Show your calculations clearly. Hint: Use the answers to the previous two questions. t = Fr t = (3.468416)*(0.059) t = 0.20464 Nm

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The next question will help you find the experimental moment of inertia of the composite object Q11: What is the experimental value of the moment of inertia of the composite object? Show your calculations clearly. Hint: Use the answers to Q04 and Q10 above. NOTE: This is the moment of inertia of the composite object about an axis passing through the point of contact with the ramp as shown in figure below.

I = t/a I = 0.20464/31.7368 I = 0.006448 Kgm^2 The next three questions will help you find the theoretical moment of inertia of the composite object Q12: What is the theoretical value of the moment of inertia of the iOLab cart? Show your calculations clearly, including the measurements of the required dimensions of the iOLab Cart. Hint: Use the formula for a 'Rectangular Prism' given here (Scroll down until Rectangular prism: moments of inertia): https://dynref.engr.illinois.edu/rem.html Be careful about the axes you need to find the moment of inertia about and, based on that, use the appropriate formula and dimensions to be used in it.

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I = 0.0000810538 kgm^2 Q13: What is the theoretical value of the moment of inertia of a single masking tape roll? Show your calculations clearly, including the measurements of the required dimensions of the masking tape roll. Hint: Use the formula for a 'Hollow Cylinder' (or ‘Cylindrical thick shell’ to be more precise) given here (Scroll down until Cylindrical thick shell: moments of inertia): https://dynref.engr.illinois.edu/rem.html Again, be careful about the axes you need to find the moment of inertia about and based on that use the appropriate formula and dimensions to be used in it. Page 14 of 17

Mass of 1 tape roll: m = 0.0914 kg Radius 1 (outside radius): 0.059 m Radius 2 (inside radius): 0.038 m I = (½)m(r1^2 + r2^2) = (½) * 0.0914 * (0.059^2 + 0.038^2) = 2.25 x 10^-4 Kgm^2

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Q14: What is the theoretical value of the moment of inertia of a composite object about the axis passing through the point of contact with the ramp? Show your calculations clearly. Hint: Use the answers to Q12 and Q13. Remember that there are TWO masking tape rolls and that the moment of inertia is an additive quantity. NOTE: The answers to Q12 and Q13 are for the moment of inertia for the axis passing through the center of mass. Whereas in Q14 you are asked to find the moment of inertia of the composite object about an axis passing through the point of contact as shown in the figure below. You will need to use the parallel axis theorem: 𝐼   = 𝐼   + 𝑀 𝑅 

[Type your answer here] Theoretical value of moment of inertia of iOLab cart: I = 0.0000810538 kgm^2 Theoretical value of moment of inertia of 1 tape roll: I = 2.25 x 10^-4 Kgm^2 Icm = 0.0000810538 kgm^2 + (2 * 2.25 x 10^-4 Kgm^2) = 5.311988 * 10^-4 Ipoc = Icm + MR^2 = 5.311988 * 10^-4 + (0.35392)(0.059)^2 = 0.001763 Kgm^2 Q15: What is the %discrepancy between the values of the moment of inertia of the composite object determined experimentally vs theoretically about the axis passing through the point of contact with the ramp? Show your calculations clearly. Hint: Use the answers to Q11 and Q14 above. [Type your answer here] Experimental value: I = 0.006448 Kgm^2 Theoretical value: 0.001763 Kgm^2 % Discrepancy = (|exp - theo| / theo) * 100 = (|0.006448 - 0.001763| / 0.001763) * 100 = 265.7 % Q16: What do you think are the reasons for the discrepancy? The reasons for the discrepancy may be because of human error, or equipment being used may not be very accurate. The human error might be from measuring the radius of the cylinder with a ruler. An error in calculations could be overlooked as well.

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LAB Group Members’ Signatures/Typed Names (Make sure all agree to “sign off” on work) Anna Popkov Sri Annepu Tylor Rauh Bennett Clark

BEFORE LEAVING, EACH PERSON IN GROUP MUST ● Get signatures/typed names of every LAB Group member in the boxes on the left OR type in their name. ● If you have printed it off, take photos of each page, and combine them into a single PDF. If you have been working in the Word file as is, then simply save it as PDF. Each person MUST upload THE SINGLE PDF File your LAB worksheet on Brightspace by 11:59 PM SATURDAY See Syllabus for LATE POLICY

ASYNCHRONOUS STUDENTS: Please paste your entire Discussion Board here (or a link to Discussion video here)

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