MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.01T Fall Term 2004 Experiment 09: Angular Momentum Purpose of the Experiment: In this experiment you investigate rotational collisions and the conservation of angular momentum in rigid body rotational dynamics. It is the rotary counterpart of Experiment 07 in which you investigated linear collisions. It is also more difficult. The heart of the experiment is a high quality DC motor to spin a rotor up to several hundred radians per second. When power to the motor is shut off, it serves as a tachometer-generator whose output voltage is proportional to the angular velocity of the rotor; thus the angular velocity of the rotor can be determined by measuring the output voltage. When you hold down the red pushbutton switch on the apparatus, power is applied to the motor; when you release it, the rotor coasts and the output voltage can be read by the DataStudio program. This experiment will give you practice in • measuring and calculating moments of inertia, • calculating rotational kinetic energy and non-conservative rotational work, and • using several other concepts from our study of rotational dynamics. Setting Up the Experiment: Plug the rotary motion apparatus into its power supply; you should see the LED in the plastic pipe elbow come on. Connect the phototransistor and generator output voltages to inputs A and B on the ScienceWorkshop 750 interface box using the leads from two voltage sensor plugs. (The generator output terminals are the two farthest from the power input connector.) The best DataStudio sampling options depend on what you are going to measure and will be given in a table for each section of the experiment. Before you can carry out any rotational collision measurements, you must first calibrate the tachometer-generator and measure the moment of inertia of the rotor. Calibrating the Generator: Stick a black sticker or a small piece of black tape on the white plastic centerpiece of the rotor so that it will be illuminated by the LED and the reflected light detected by the phototransistor. The voltage output will be about 5 V when the LED is reflected from the black tape and 1 V when it is reflected from the white plastic. Set up the DataStudio sampling options as follows. Voltage Sensitivity Voltage Sample Rate Delayed Start Automatic Stop Low (1X) 5000 Hz None 0.25 sec Set up graphs to plot both the phototransistor output and the generator output as a function of time. Spin the motor up for several seconds, release the button and allow it to coast for about a second, then click the DataStudio start button. Experiment 09 1 November 15, 2003You should get plots something like these. The voltage peaks on the left graph correspond to the black tape passing in front of the LED. The number of peaks you see depends up on how fast the rotor was spinning when you did your measurement; anywhere from five to ten peaks in the 0.250 s plot time should be OK. Use the graph Smart Tool (locked on to the points) to find the time for, say, six revolutions of the rotor. The generator output in the right graph is noisy, but you can select the data corresponding to the time period between the peaks you counted in the left graph and use the Σ tool for the generator graph to find the average output voltage for the period. Use these results to find the angular velocity and voltage generator output. (You should find that 1 V corresponds to about 70 radians/sec; I obtained 71.8 (rad/s) V−1.) Record your value in your report. If you were fussy, you could repeat the measurement for several different rotation speeds, but I checked it and found it to be quite linear—so there is no real need. Remove the black sticker or tape. In the remaining measurements you will only use the generator output voltage and can remove the graph of phototransistor output. Finding the Rotor Moment of Inertia: Next, you must measure the moment of inertia IR of the rotor. To do this you will use a 55 gm weight (50 gm brass weight plus 5 gm plastic holder) to accelerate the rotor. Tie a loop in one end of the string and use it to suspend the weight over the pulley, as shown in the photo at the top of the next page. Use a string just long enough to reach from the weight (when it is on the floor) over the pulley to the axis of the rotor. Tie a knot at the other end of the string and insert the string into the kerf cut into the brass washer on the rotor and wind the string around the constant diameter portion of the white plastic. (This part has a diameter of 1.00 inch or a radius of 12.7 mm, which you will need to calculate the torque.) Keep the string away from the Velcro on the washer that is part of the rotor as you wind it. Set up the DataStudio sampling options as follows. Voltage Sensitivity Voltage Sample Rate Delayed Start Automatic Stop Low (1X) 500 Hz None 4.0 sec Experiment 09 2 November 15, 2003Click the DataStudio start button and release the weight. You should get a graph that resembles the one below. The graph has two feaures. First the voltage (ω of the rotor) increases linearly, showing constant angular acceleration α. Then it shows a constant (but smaller in magnitude) angular deceleration. The change from one to the other comes w hen the string pulls out of the kerf. Experiment 09 3 November 15, 2003The constant deceleration is produced by a constant f riction torque τf , and the acceleration is produced by the torque from the 55 gm weight. Of course friction also acts when the falling weight is accelerating the rotor, so you will have to know τf in order to find the moment of inertia of the rotor. A Linear Fit separately to the rising and falling parts of the graph will give the answers. You may be unlucky and the string will not pull cleanly out of the kerf and allow the rotor to coast. In that case you can still obtain the angular acceleration αup for the rising curve on the left in your graph but you should make a second measurement to get the angular acceleration αdown when the rotor is slowing down under the torque of the bearing friction. To do that, remove the string from the rotor, spin up the motor with the red power button, release the
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