Lab 08 - Rotational Inertia of a Pulley

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Dec 6, 2023

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Lab 8: Rotational Inertia of a Pulley Name : _Brandon Cook_______________________________ In this lab we are going to explore the moment of inertia (also known as rotational inertia) of a pulley by comparing the experimental moment of inertia obtained in a virtual experiment and the corresponding theoretical moment of inertia. Before going to the procedure, we must obtain an expression for the tension T acting on a moving pulley due to the weight of the hanging mass in the next figure, because it is this tension the force that exerts a torque on the pulley: Applying the second law of motion (ΣF = ma) to the hanging mass m, we have that: T – mg = m (–a), so the tension is given by: T = m(g – a). If the outer radius of the pulley is R 2 , then the torque exerted by the tension on the pulley is  = R 2 T sin 90° = R 2 T. Rotational Inertia of a Pulley 1. Please click on the following link to access the browser-based simulation we need to do this lab activity: https://www.thephysicsaviary.com/Physics/Programs/Labs/UnwindingCableLab/ 2. Click on “Begin”. The virtual experiment will be done under the conditions of planet Earth, so make sure that on the right upper corner of the screen it says “Earth”. If the name of a different planet appears, click on it until it shows “Earth”. AGB_DallasCollege

Lab 8: Rotational Inertia of a Pulley 3. Write in the experimental data sheet the following quantities: the mass m of the hanging or falling mass, the mass M of the pulley, the outer radius R 2 of the pulley, and the inner radius R 1 of the pulley. 4. Click on “Start” and, after the falling mass reaches its lowest position, go to the velocity versus time graph at the bottom of the webpage. The initial time at which the hanging mass starts falling is zero, so the elapsed time (time interval) Δt it takes for the mass to reach its lowest point is the time corresponding to the last data point on the velocity versus time graph, which is the final time t f . For example, in the figure below, we can estimate that t f = 0.515 s. Write your value for the final time t f in the experimental data sheet. 5. Read on the velocity versus time graph the absolute value of the final velocity v f of the hanging mass, which is the velocity corresponding to the final time t f . For example, in the figure below, we can estimate that v f = 1.54 m/s. Write your value for v f in the experimental data sheet. NOTE: Your values for the quantities t f and v f will be different from the ones in the figure above. AGB_DallasCollege

Lab 8: Rotational Inertia of a Pulley 6. Calculate the magnitude of the downward acceleration a of the hanging mass using the equation a = v f /t f , and write this value in the experimental data sheet. 7. Calculate the tension T using the equation T = m(g – a), and write this value in the experimental data sheet. 8. Calculate the torque  acting on the pulley using the equation  = R 2 T, and write this value in the experimental data sheet. 9. Calculate the angular acceleration α of the pulley by using the equation α = a/R 2 , where a is the acceleration calculated in step 6, and write this value in the experimental data sheet. 10. Using the equation I exp =  /α (obtained from the rotational second law of motion, Σ  = I α), calculate the experimental moment of inertia I exp and write this value in the experimental data sheet. 11. Calculate the theoretical moment of inertia I the of the pulley using the equation: I the = ( 1 2 ) M ( R 1 2 + R 2 2 ) , and write this value in the experimental data sheet. AGB_DallasCollege

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Lab 8: Rotational Inertia of a Pulley Name: _Brandon Cook____________________________________ EXPERIMENTAL DATA SHEET Hanging or falling mass m = _______100_____ kg Mass of pulley M = ______500______ kg Inner radius of pulley R 1 = _____90______ m Outer radius of pulley R 2 = _____100______ m Final time t f = _____.670_____ s Final speed v f = ___1.19________ m/s Acceleration (magnitude) of hanging mass a = ___1.17_________ m/s 2 Angular acceleration of pulley α = ____.0117_______ rad/s 2 Tension on string T= ______863______ N Torque on pulley  = ____86300_______ N  m Experimental moment of inertia I exp = ____7376068________ kg  m 2 Theoretical moment of inertia I the = _____4525000_______ kg  m 2 AGB_DallasCollege

Lab 8: Rotational Inertia of a Pulley Questions 1 . Calculate the percent of error of the experimental moment of inertia relative to the theoretical moment of inertia using the equation % error = ( | I exp − I the | I the ) x 100 . Include the steps. Answer: % error = ( | 7376068 − 4525000 | 4525000 ) x 100 . % error = 63.01 % 2a . If the pulley in this experiment was a uniform solid disk instead of the one used, how would that affect the value of the experimental moment of inertia? [Assume both pulleys have the same mass and outer radius.] 2b . Calculate the theoretical moment of inertia of a solid uniform disk with the mass and radius equal to the mass M and the outer radius R 2 of the pulley used in this experiment. AGB_DallasCollege

Lab 8: Rotational Inertia of a Pulley AGB_DallasCollege

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