R E W R I T E this lab in your O W N words, in correct lab format. however, do not change the values and do not copy the words used in this lab. Introduction: Due to its similarity to linear dynamics and derivation from Newton's Second Law, rotational dynamics is useful in physics. Torque controls the rotational velocity, which is determined by the moment of inertia times the angular acceleration, just as force and velocity are directly related. Accordingly, the moment of inertia becomes the "mass" of rotational dynamics, whose characteristics-specifically, its dependency on weight distribution-can be examined using a three-step pulley system, a hanging mass, and varying the weight on the largest pulley. By watching the variations in angular acceleration when the weight distribution (or radius) of the bigger pulley varies, the three-step pulley with a hanging mass provides the data needed to compute the moment of inertia (1). The following equation can then be used to get the moment of inertia: I = / = mr(g-r )/ In order to ascertain the link between the moment of inertia and weight distribution and provide a response to the question of how the distribution of mass influences the moment of inertia, the experimental moments of inertia computed from Equation 1 can then be shown on a graph. Procedure: Apart from the post-experiment analysis, there are two main steps to this experiment. The first step is the process of setting up the experiment. Begin by setting up the three-step pulley, and tying a string, about a meter long, onto the larger pulley on the Rotary Motion Sensor. By calculating the masses of each weight and the rod separately, prepare the rod at 40.0g and the weights at 80.6g and 80.5g. Next, measure the distance between the weights that are attached on the opposite sides and equally spaced from the center. To prepare the hanging mass, add a mass of between 10 and 30 g to the hanger, which weighs about 15 g. The overall mass should be between 25 and 45 g. After tying the hanging mass to the other end of the string, attach it to the three-step pulley (see figure 1 above). Last but not least, get LoggerPro ready to start collecting data. The second step is the actions involved in carrying out the experiment and gathering data. Start data collection, wind the string onto the motional sensor's biggest pulley, and then let go of the weight. The slope of the angular velocity vs. time graph can be used to calculate the angular acceleration. Five more times, repeat this experiment, varying the distance between the weights and the center of rotation each time. Finally, use eq. 1 to determine the moments of inertia for each run and compile the results on a graph for further study. Results: Six trials were used to gather data at various radius lengths (r), all between the rod's center of rotation and its end. The data collected from each run, which makes up each trial, was utilized. Included here are the angular accelerations and uncertainty brought on by the angular velocity vs. time graphs' slope. (see Diagram 3 in the appendix). For each trial, the effects of friction and air resistance are assumed to be negligible. The calculation for the moment of inertia is shown in Figure 1. Equation 1 was used to compute all moments of inertia. The experimental data from the runs, including the angular accelerations and the weights' radius (r), are shown in Diagram 3. Figure 2 displays all moments of inertia computations as well as the values for the "constants," or additional variables, such as the mass (m), radius (r), and acceleration due to gravity (g) that are required for the calculation. The resulting graph of the moment of inertia (I) vs radius squared (r^2) is shown in Diagram 2. The radius was ultimately squared to linearize the graph which was used for further analysis of the relationship between inertia and the weight distribution on the rod. Discussion: When the estimated moments of inertia and their corresponding radii are squared, the slope of the graph shows a linear relationship. The experimental value of the slope, which was 0.1661 kg*m^2/m^2 +/-0.012 kg*m^2/m^2 is also depicted in this graph. This value likewise led to a non-negligible y-intercept of 0.00071 +/-0.0002 kg*m^2. From this, it can be seen that when the radius r is 24mm, or the distance between the weight and the center of rotation, is small, for example 3.75 cm, the angular acceleration is faster than that of a larger radius R 155mm. The resulting graph (Diagram 2) illustrates that when the radius is on the smaller side, there is a smaller moment of inertia. This causes a significantly smaller moment of inertia. The distribution of mass on the system of interest is observed to have a direct relationship and dependence on the moment of inertia in that a bigger distribution of mass results in a greater resistance to motion. Conclusion: Overall, the findings show that the size of the weight distribution affects the amplitude of the moment of inertia. This may be observed in the graph created using the calculated experimental moments of inertia and the direct correlation between the angular velocity and the weights' radius. There is a non-negligible y-intercept to take into account, demonstrating that inertia exists even when the radius is zero. There may be this in the results, along with other possible random or systematic errors. The scales, rotating motion sensor, and other pieces of equipment may be to blame for such a potential random error. The way the measurements were obtained or the way the three-step pulley was set up may have increased inaccuracy, which is a probable systematic error. By using the same setup and process for every trial and maintaining consistency with measuring the slopes of the angular velocity vs. time graphs, an effort was made during the experiment to reduce this kind of inaccuracy. To further reduce potential causes of stated systematic inaccuracy, it is advised to utilize more precise measuring tools and constant push forces. It is advised to conduct more research to validate or refute these conclusions. , t