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# RKE - RKE Rotational Kinetic Energy revised Learning...

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1 Rotational Kinetic Energy RKE Rotational Kinetic Energy revised July 11, 2005 Learning Objectives: During this lab, you will 1. communicate scientific results in writing. 2. estimate the uncertainty in a quantity that is calculated from quantities that are uncertain. 3. be introduced the Monte Carlo Simulation method. 4. test a physical law experimentally. A. Introduction You will use the principle of conserva- tion of energy to determine the moment of inertia of a system of four identical masses symmetrically located on the circumference of a wheel which is rotating about its axis (Figure 1). You will compare the value you measure to the value you calculate from theory. Because the wheel has a complicated shape, you must measure rather than calcu- late its moment of inertia. You can also measure the combined moment of the wheel and the mass loads and then calculate the moment of inertia of the loads alone as the difference between these two measurements. This experiment also includes an intro- duction to a numerical method that may be new to you - Monte Carlo computer simula- tions. Monte Carlo simulations are used to study phenomena where random chance is expected to play a major role. Randomness is also a feature of the experimental errors than one often encounters. You will use a Monte Carlo simulation for the RKE experiment to create data for debugging and testing your analysis routine. You will then apply this analysis routine to experimental data collected from the inertia wheel and mass loads. You must write a report for this lab worth 60 points. B. Apparatus Neighboring groups will share a single setup, but each group must acquire and ana- lyze their own set of data. It takes very little time to take the data you need for this experiment so sharing a single setup should not be a problem. Before taking any data, be certain that the cable from the encoded pul- ley is plugged into the jack on your own computer station. The key piece of apparatus is a Roto- Dyne inertia wheel [ mass M R = 1.5 kg, radius r = 0.200±0.002 m ] on which you can mount four cylindrical mass loads [ M L = 0.225±0.002 kg each ]. The torque necessary to rotate this wheel will be supplied by grav- ity acting on a hanging mass [ M = 60 g ] and some paper clip masses, m . You will also use a meter stick, an encoded pulley and a computer running the Logger Pro program. The experimental setup is illustrated in Figure 1. The hanging mass M is tied to a string hanging over an encoded pulley and wrapped around the grooved circumference of the wheel. The encoded pulley records Encoded Pulley Roto-Dyne inertia wheel W=Mg Loads Loads Figure 1: Experimental Arrangement

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