MASSACHUSETTS INSTITUTE OF TECHNOLOGYPhysics DepartmentPhysics 8.01 Fall Term 2007Experiment 05: Angular MomentumPurpose of the Experiment:In this experiment you investigate rotational collisions and the conservation of angularmomentum in rigid body rotational dynamics. It is the rotary counterpart of linearcollisions.The heart of the experiment is a high quality DC motor to spin a rotor up to several hundredradians per second. When power to the motor is shut off, it serves as a tachometer-generatorwhose output voltage is proportional to the angular velocity of the rotor; thus the angularvelocity of the rotor can be determined by measuring the output voltage. When you holddown the red pushbutton switch on the apparatus, power is applied to the motor; when yourelease it, the rotor coasts and the output voltage the motor generates can be read by thecomputer. This experiment will give you experience in• measuring and calculating moments of inertia,• calculating rotational kinetic energy and non-c onservative rotational work, and• using several other concepts from our study of rotational dynamics (including theconservation of angular momentum, conservation of rotational kinetic energy and thekinetics of rotational motion when the angular acceleration is constant) to deducequantities that you cannot measure directly.Setting Up the Experiment:Plug the rotary motion apparatus into its power supply; you should see the LED in theplastic pipe elbow come on.Experiment 05 1 November 14/15, 2007The experiment is longer than any we have done before and has two parts; extra time hasbeen allotted to do it. First, you will calibrate the equipment and measure the momentof inertia of the rotor. Second, you will use the calibrated apparatus to study rotationalcollisions.At the start of the experiment, use two voltage sensor plugs to connect the output fromthe apparatus to inputs A and B on the SW750 interface box. Connect the generatoroutput voltage (the jacks farthest from the power input connector) to input A and thephototransistor output to input B.The data acquisition and analysis for both experiments will be done with the LabVIEWprogram called AngularMomentum.exe.The program operation is controlled by the main pull-downmenu at the upper left of the graph and the three tabs la-beled “Graph”, “Run and Fit Parameters” and “Calibrate” onthe front panel. The Calibrate tab is an addition to what youhave become used to our previous LabVIEW programs. It isthere because two calibrations must be done in this experiment.Before you can carry out any rotational collision measurements,you must first calibrate the tachometer-generator and then mea-sure the moment of inertia of the rotor. These are the tasks ofPart I; in Part II you will study rotational collisions.The first calibration is to calibrate the tachometer generator output, i.e., what is ω for 1 Voutput ? When the Calibrate tab is active (that means it’s the one whose contents you cansee) and the “Which Calibration?” pull-down menu on the tab is set to Tachometer, theprogram will measure the voltages on channels A and B and assume that data files savedby or read into the program contain two voltages as a function of time. Also, the Fit Dataoption of the main pull-down menu will use these two voltages to calibrate the generator,in a way that you will see presently.Otherwise—when the Calibrate tab is not active (visible) or it is active with the pull-downmenu on the tab set to Moment of Inertia—the program measures only the voltage oninput channel A and uses the generator calibration result to convert the voltage to angularvelocity; then the Fit Data option will fit ω to A + Bt; and data files saved by or read intothe program will contain only angular velocity as a function of time.Cursor Control:This widget above the graph helps you position the cursor more accu-rately. The button in the middle lets you select which cursor moves.The arrows move the cursor one data point each time you click them. (On Windowsmachines the keyboard left and right arrow keys do the same thing.) You can still positionthe cursors by dragging, but this may be easier for precise movement.Experiment 05 2 November 14/15, 2007Part I: CalibrationCalibrating the Generator:Put a black sticker on the white plastic centerpiece of the rotor so that it will be illuminatedby the LED; the reflected light will be detected by the phototransistor. (The voltage outputwill be higher when the light is reflected from the black tape and lower when more light isreflected from the white plastic.)Set the voltage sample rate to 5000 Hz from the pull-down menu and type a run time of0.25 (s) into the window. For this calibration you want to measure both the phototransistoroutput voltage and the voltage from the generator. Then perform the following steps.1. Click the Calibrate tab and make sure the “Which Calibration?” pull-down menu isset to Tachometer.2. While the Calibrate tab is still active (visible) choose Measure from the main pull-down menu; the START button will become brighter green, indicating the program isready to make the measurement.3. Spin the motor up for several seconds, release the red button and allow the motor tocoast for about a second, then click the START button (or type the Esc key on thekeyboard). The START button will briefly turn red and say STOP while the computermakes the measurement.After the measurement is over, click the Graph tab and you will have a plot of the twovoltages, as in the figure below. The purple curve (Plot 0) is the generator output voltageand the green one (Plot 1) is the phototransistor voltage.Experiment 05 3 November 14/15, 2007To calibrate the generator, you need to find the time between the first and last fully visiblephototransistor peaks on the graph. Here is how to do that.1. Place one cursor at the center of the first complete voltage peak and the other at thecenter of the last complete voltage peak of the phototransistor output. You can dothis roughly by dragging the the cursor onto the peak. Then use the zoom control(center button on the graph palette) to expand each peak in turn and position eachcursor more accurately in the center of the peak.2. Next, count the number of rotation periods between the two peaks; then click theCalibrate tab. You can type in the likely errors in the voltage (Sigma V) and time(Sigma T) me asurements, but the default σV= 0.01 V and σT= 0.0005 s are OK.3. Make sure the
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