Mini Lab #8

Laboratory Report: Lab Date: October 31, 2023 Experiment Title: Rotational Motion and Moment Inertia Course/Section #: PHYS 201-400 Station #: 11 Names of the people (who performed the experiment): Natalie Hesterman & Holly Pawlowski & Alejandro Mapula Names of the missing students: N/A TA’s Name: Mahmodul Maheen Lab Partners: Natalie Hesterman & Holly Pawlowski & Alejandro Mapula

Introduction: In this experiment, we studied the relationship between the torque and the angular acceleration as described by Newton's Second law of rotational motion. In the two previous labs, we studied transitional motion where the acceleration and the force are in the same direction as the motion’s direction, which leads to linear motion. In this case, the force was not in the same direction as the motion, which gives rise to the idea of rotational motion. In this lab, we completed two activities. In both of these activities, we used a Verinir Rotary Sensor to measure the angular displacement, the LoggerPro Mini Quest, a spindle/screw to attach Disk “A” to the three-step pulley, a three-step pulley, a ring stand, a balance, a lightweight mass hanger, masses, and a string. For this experiment, we familiarized ourselves with two equations: 1. t=Ia 2. I(m)=I(0)+I(p)+m*R(s)^2 Results: Table 1. Disk "A" Disk "B" Mass (M) 105 g 107 g Disk's Radius (R) 4.5 cm 4.5 cm Moment of Inertia of a disk: I(0)=1/2MR^2 1.063e^-4 1.08e^-4 Table 1 shows the masses of each disk from the rotary motion sensor, along with the disk’s radius and the moment of inertia of each disk. Table 2. Summary of the measured values Case #1: (25g) Case #2: (55g) Case #3: (105g) Case #4: (55g) Case #5: (105g) Angular Acceleration a(rad/s^2) 47.85 92.4 146.8 52.51 88.82 Tourque= MhgR^m_s 0.006125 0.013475 0.025725 0.013475 0.025725 I_m=Tourque/a 1.28e^-4 1.46e^-4 1.75e^-4 2.57e^-4 2.90e^-4 Table 2 shows 5 different case trials with different pulley masses. It shows the angular acceleration, the torque value along with the moment of inertia. Table 3. Summary of measured and calculated values of moment inertia Case #1 Case #2 Case #3 Case #4 Case #5 Measured Moment of Inertia (I_m) 1.28e^-4 1.46e^-4 1.75e^-4 2.57e^-4 2.90e^-4 Calculated Moment of Inertia (I_c) 1.23e^-4 1.426e^-4 1.739e^-4 2.51e^-4 2.82e^-4 Table 3 highlights each of the 5 case trials along with their measured moment of inertia and the calculated moment of inertia.

hanging mass go off the table. This sometimes resulted in a large impact on the ground and it could account for the errors. In conclusion, we feel that this lab taught us a lot about the moment of inertia, which is very useful in today’s world. We were able to learn more about Newton’s Second Law and familiarize ourselves with how to calculate moments of inertia via equations. Our results above seem to be pretty accurate, however, we feel that some reasons for errors could have been due to the realization of the hanging mass on the pulley, which could have led to some data collection errors.