F23_Lab 7-2

Lab 7: Moment of Inertia—Informal Report Questions Q1: Comparing Eq. 7.1 to F = ma . Which terms are analogous to each other? In equation 7.1, the terms of the moment of inertia ( I ) and the resistance to angular rotation ( α ) are analogous to mass ( m ) and linear acceleration ( a ) respectively. Q2: Consider a ring and a disk of the same mass and outer radius, both rotating around their center of mass horizontally. Which object will have a larger amount of inertia? The ring will have a larger amount of inertia because, in the instance of the ring, the equations take into account the inner radius of the ring. The equation for the disk does not have this 4th variable so the contribution of the 4th variable will likely increase the amount of inertia experienced by the ring. Q3: If the axis of rotation is moved away from the center of mass for an object, how would the moment of inertia change? The moment of inertia would increase if the axis of rotation is moved away from the center of mass for the object. This means that it would be very challenging to change the rotation speed of the object. Q4: Knowing the units of torque from Eq. 7.2 and moment of inertia from Eq. 7.3, what are the units of angular acceleration α ? The units of angular acceleration are I/s 2 . Q5: What is the equation you derived? (Make sure that your equation only depends on quantities that can be directly measured.) 𝐼 = 𝑚? 2 ? 𝑔 − ? ( ) Q6: What are your experimental values for the moment of inertia? Table 7.1: Expected and experimental moment of Inertia for the objects used in this lab Horizontal Disk Horizontal Ring Vertical Disk I expected (kg/m 2 ) 0.0360 0.00490 0.0181 I experimental (kg/m 2 ) 0.0924 0.0447 0.0574 Q7: Are your experimental and expected values in agreement with each other? Discuss in detail each of the three different experiments. The experimental and Expected values are mostly in agreement with one another. In the horizontal disk experiment, the expected value of the moment of inertia was 0.0360 (kg/m 2 ) as compared to the experimental value of 0.0924 (kg/m 2 ). In the vertical disk experiment, the expected value of the

moment of inertia was 0.0181 (kg/m 2 ) as compared to the experimental value of 0.0574 (kg/m 2 ). The trials with the horizontal ring varied the most as this was the more challenging of the experiment and had the most room for random error such as in the calculations. Finding the experimental value here involved the subtraction of the experimental value for the horizontal disk from the data that was collected using the combination of the horizontal disk and the ring. Here the experimental value of the moment of inertia was found to be 0.0447 (kg/m 2 ) as compared to an expected value of 0.00490 (kg/m 2 ). Q8: A source of error in this experiment is friction, both in the pulleys and the rotating platform. Would you expect friction to make your experimental values for moments of inertia higher or lower? Can you think of other sources of error in your experiment? I would expect friction to make our experimental values higher than our current results. Our values would be physically higher, because the moment of inertia describes the resistance of an object to rotational force and friction will increase the resistance. Other possible sources of error could be found when transcribing data, there may be a lower level of data accuracy due to the divide of labmates that collected the data versus transcribed the data (aka. tasks were split up throughout the experiment, which may have caused inconsistencies). Free Body Diagrams Figure 1. Free body diagram of the mass hanger and rotating platform. Most forces are isolated and occur on the mass hanger.