PHYS Lab 6 Report

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Physics

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Apr 3, 2024

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Fatima Vazquez Patricia Rubio Asia Moton Lab 6 Report Introduction: Our group is trying to find the moment of inertia in the y direction. In order to do so we set mgh (the gravitational potential of the iolab) = to ½ mv^2 + ½ Iw(angular velocity). By setting up the conservation of energy = to the equation of kinetic energy with rotation. We can say that the conservation of energy is mgh or gravitational potential energy because there is no initial kinetic energy present. The mass is equal to 0.2 kg and we know that g = 9.8 m/s^2. By measuring the length of the ramp in the y direction plus the height of the iolab with the rolls we obtain height to be .17399 m. We don't know v, so we plug in w(angular velocity) times R(the radius of the iolab which is .0381 m). From this we can measure the angular velocity in our experiment and then solve for the moment of inertia in the y direction. Methods; In order to solve for the moment of inertia, we will set up a ramp and insert the iolab into two rolls of tape on each of its sides. Then we rolled the device with the rolls of tape down the ramp to measure the angular velocity. Since we are using the conservation of kinetic energy we determine the maximum angular velocity which is where the device reaches the bottom of the ramp (angle is equal to zero). Results: Trial 1: Trial 2:

Trial 3: Analysis: Formulas used: v=ωR mgh = mv 2 + Iω 2 → I = 1 2 1 2 2(𝑚𝑔ℎ− 1 2 𝑚𝑣 2 ) ω 2 Trial 1: V = (27.888)(0.0381) =1.06 I = = 0.000588 2((0.2)(9.8)(.17399)− 1 2 (0.2)(1.06 2 )) 27.888 2 Trial 2: V = (29.402)(0.0381) = 1.12 I = = 0.000499 2((0.2)(9.8)(.17399)− 1 2 (0.2)(1.12 2 )) 29.402 2

Trial 3: V = (30.349)(0.0381) = 1.16 I = = 0.000448 2((0.2)(9.8)(.17399)− 1 2 (0.2)(1.16 2 )) 30.349 2 Uncertainty Calculations: Standard deviation = (0.000588-0.000448)/2 = 7E-5 Standard error = 7E-5/ = 4.04E-5 3 Uncertainty = 5.12E-4 4.04E-5 ± Discussion: Upon completing our data calculations, we did not find it surprising that the moment of inertia is small because the radius measured was so small therefore creating a small moment of inertia. The results between trials were fairly consistent having a standard error of only 4.04E-5. Conclusion (Assumptions): In our experiment we assumed that the iolab device would roll without slipping in order to use the equation v=wR to solve for velocity. To minimize this assumption we made sure the iolab would roll without being disturbed so as to accurately calculate the angular velocity. We also discussed how the rolls of tape have mass to them and can affect the overall mass, therefore affecting the inertia. In addition, having the mass of the rolls be as small as possible would help us get a better estimate of the moment of inertia but there was nothing much that we could do to minimize them. Through our experiment we found that the moment of inertia varied from 0.000588 to 0.000448 and we calculated this by taking the angular momentum of our iolab device found through rolling the device down the ramp and using the angular momentum of its highest point. With this we then plugged our radius of the iolab, height of ramp+iolab, and the mass of the iolab into the equation mgh=1/2mv^2+1/2Iw(angular speed)^2 to calculate the inertia. Contributions: We all contributed to the introduction, experiment, results, and conclusion.

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