PHYS172_S21-Lab10-butomo

PHYS 172 LAB 10 ANGULAR MOMENTUM PRINCIPLE : Finding Moment of Inertia SPRING 2021 LAST NAME (ALL CAPS): _____UTOMO__ FIRST NAME (ALL CAPS) _____BRAMANTIO_________ PUID:_0032539685_ LAB Section DAY _____W_____ LAB Section TIME ___3.30-5.20____ LAB GROUP#__6__ (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. Force = M*g M = F/g M = 1.516 / 9.81 M = 0.154 kg TAKE A PHOTOGRAPH OF THE SET UP YOU USED TO FIND THE MASKING TAPE ROLL MASS. PASTE IT BELOW

Page 2 of 9 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)

Page 4 of 9 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) With a bigger angle the torque will be greater, however if the angle is too big, the friction that is created between the tape and the surface may not be strong enough for it to generate torque, and it would just slide forward. (b) the angle will has a great importance when it comes to the torque and inertia itself as the only force acting on the object is weight, and since it is in an incline then the force is divided into its x and y components in relation to that angle, meaning it will impact the magnitude of the force creating the torque. As the angle increase the inertia force will also increase.

Page 5 of 9 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 . The axes that is relevant to the rotation of the iOLab is the y axes. This is because it is where the axes of rotation of the iOLab is. 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 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)

Page 7 of 9 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 . Torque = angular acceleration * moment of rotational inertia 0.101493 = 26.5784 rad/s 2 * moment of inertia Moment of inertia = 0.00381863 kg*m/s 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. IOLab x length = 7.5 cm IOLab z length = 2.7 cm Ic,y = (1/12)*m*((l z ) 2 +(l x ) 2 ) Ic,y = (1/12)*(0.242kg)*((.027 m) 2 +(.075m) 2 ) Ic,y = 1.28*10 -4 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. Ic,y = (1/2)*m(r 1 2 + r 2 2 ) m = 0.154 kg r 1 = 0.03726 r 2 = 0.0595 m Ic,y = (1/2)*(0.154)( 0.03726 2 + 0.0595 2 ) Ic,y = 3.795*10 -4

Page 8 of 9 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?? ?? 𝑐???𝑎𝑐? = 𝐼 𝑐????? ?? ?𝑎?? + 𝑀 𝑇??𝑎? 𝑅 2 I center of mass = I IOLab + 2*I Masking Tape I IOLab = 1.28*10 -4 I Masking Tape = 3.795*10 -4 I center of mass = 1.28*10 -4 + 2 * 3.795*10 -4 I point of contact = I center of mass + MR 2 M = 0.55 kg R = 0.0595 m I point of contact = (8.87 * 10 -4 ) + (0.55) * (0.0595) 2 I point of contact = 2.83 * 10 -3 kg*m/s 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. %discrepancy = (experimental – theoretical) / theoretical * 100% Experimental = 0.00381863 kg*m/s Theoretical = 2.83 * 10 -3 kg*m/s %discreapncy = (0.00381863-(2.83 * 10 -3 )) / (2.83 * 10 -3 ) = 34.93 % Q16: What do you think are the reasons for the discrepancy? The torque can be affected by friction, and in this experiment friction is not accounted. The experimental value of inertia is higher than our theoritical value because our calculated value assumed that all of the torque pushing the system down. While in practice, the torque minus the friction was pushing the system down. Using a torque without subtracting friction would result in a higher moment of inertia.