Lab report 2

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Apr 3, 2024

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Tiller, Cadence Partner: Treadway, Luke Moment of Inertia TA: Pandey, Kumar, Section #3 Date Performed: April 17, 2023 Objective : The objective of this experiment is to determine the moment of inertia of the rotating system by We manipulated the experiment by adding mass to the hanger and on the system. We then had to accurately determine the new moment of inertia. Moment of inertia is defined as the rotational analog of mass. Newton’s second law states that the acceleration of a body is directly proportional to the vector sum of all forces applied to the body (F= ma ). Moment of inertia is derived from this equation τ = Iα. When an object experiences a constant angular acceleration, it must be under the influence of a constant torque. This is similar to how constant linear acceleration implies a constant force acting on an object. In rotational motion, the relationship between torque, moment of inertia, and angular acceleration is given by τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration. This equation can be used to determine the moment of inertia of a rigid body by measuring the torque applied and the resulting angular acceleration. Then, by rearranging the equation τ = Iα, you can solve for the moment of inertia I. The Moment of Inertia equation is I = t/  . The independent variable in this experiment are the masses added to the hanger and the rotating system, and the dependent variable is the moment of inertia. Data and Analysis:

In this experiment, we began by measuring the diameter of the axle ( D axle ) with the venier caliper. We found the radius of the axle ( r axle )by dividing the diameter by two. We then used a meter stick to measure the distance from the bottom of the mass hanger to the floor which represent our y floor. We found the R masses by measuring the distance from the center of the disk to the outer set of tapped holes. We used a stopwatch to measure the time it took for the hanger to fall to the floor. We found the average time by adding all the trials up and dividing by five. In part 1a, we measured the time it took for the hanger (0.05 kg ) to fall to the ground. In part 1b, we added an additional 100 g (0.1 kg ) to the hanger and measured the time it took for the hanger to fall the ground. In part 2, we added three masses to the disk which are 1.35 kg each. In part 2a, we used the mass of the hanger (.05 kg ), and in part 2b we added the additional 100 g (0.1 kg ) and measured the time it took for the hanger to reach the ground. From this we were able to calculate the linear acceleration, angular acceleration, tension, and torque. D axle : 0.056 m r axle : 0.028 m Y floor : 0.848 m R masses : 0.172 m Raw Data: Trial t-Part 1 (a) (s) t-Part 1 (b) (s) t-Part 2 (a) (s) t-Part 2 (b) (s) 1 12.08 ( s ) 6.74 ( s ) 26.90 ( s ) 15.48 ( s ) 2 11.88 ( s ) 6.95 ( s ) 26.47 ( s ) 15.55 ( s ) 3 12.42 ( s ) 7.21 ( s ) 27.20 ( s ) 15.22 ( s ) 4 12.36 ( s ) 7.03 ( s ) 26.49 ( s ) 15.73 ( s ) 5 11.74 ( s ) 6.63 ( s ) 26.81 ( s ) 15.73 ( s )

Average 12.24 ( s ) 6.91 ( s ) 26.78 ( s ) 15.54 ( s ) Calculated Data: Part 1 (a) Part 1 (b) Part 2 (a) Part 2 (b) a 0.011 m / s 2 0.035 m / s 2 0.002 m / s 2 0.007 m / s 2  0.392 rad / s 2 1.29 rad/s 2 0.07 rad/s 2 0.25 rad/s 2 T 0.489 N 1.46 N 0.49 N 1.46 N t 0.013 N * m 0.04 N * m 0.013 N * m 0.04 N * m Calculations: a = 2  y /t 2  = a / r T = m (g – a ) t = rT Part 1 (a): a = 2(0.848 m ) / (12.24 s ) 2 = 0.011 m / s 2  = 0.011 m / s 2 / 0.028 m = 0.392 rad/s 2 T = 0.5 kg (9.8 m/s 2 – 0.011 m/s 2 ) = 0.489 N t = 0.028 m * 0.489 N = 0.013 N * m Part 1 (b): a = 2 (0.848 m ) / (6.91 s ) 2 = 0.035 m/s 2  = 0.035 m/s 2 / 0.028 m = 0.392 rad/s 2 T = 0.150 kg (9.8 m/s 2 – 0.035 m/s 2 ) = 1.46 N

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