EXPERIMENT 9 Energy Conservation in Rotation Figure 9-1: The Rotational Inertia ApparatusINTRODUCTION In this experiment a horizontal crossbar is set into rotation about a vertical shaft passing through its center. The crossbar is loaded with masses at given distances from the axis of rotation. The rotation is produced by a string wound around the axis and passed over a pulley, then attached to a suspended mass which is allowed to fall under the influence of gravity (see Figure 9-1). As the suspended mass falls, the resulting tension in the string produces a torque on the vertical shaft, giving a rotational acceleration to the crossbar and loaded masses. Analyzed in terms of energy conservation, the decrease in potential energy of the falling mass is accompanied by a corresponding increase both in linear kinetic energy of the falling mass and in rotational kinetic energy of the crossbar, loaded masses, and vertical shaft. This principle is used to determine the moment of inertia of the loaded masses, and the result compared to the value predicted by theory. PROCEDURE P1. Carefully compare the equipment provided with that shown in Figure 9-1. Use the small spirit level to level the base of the apparatus. Measure the diameter of the vertical shaft with the vernier caliper. Be sure to include the string. Half of this diameter will give a measure of the distance from the center of the shaft to the center of the string, which is the radius (r) of the shaft needed for the calculations. P2. Attach the crossbar to the vertical shaft, centering it as well as possible. Fix a 100-gram slotted mass to each side of the crossbar about 10 em from the vertical shaft, using the wingnuts provided. Measure this distance carefully. This distance from the center of the vertical shaft to the rotating masses will be labeled R. P3. Tie one end of a string about 130 cm long to the screw eye fixed to the vertical shaft. Pass the string over the pulley and fix the free end to a weight hanger. Add about 200 grams to the hanger and record this value as m. Rotate the vertical shaft so as to wind the string around the shaft and raise the hanger until the top of the hanger is near the pulley. Prevent the hanger from falling until you are ready to take data. P4. When you are ready to take data, release the hanger and at the same moment start the timer. When the hanger reaches the end of its fall, stop the timer. Record the time of fall as t. Use a meter stick to determine the distance of fall (h). P5. Repeat P4 several times to obtain good average values of time and distance. P6. Remove the masses from the crossbar, but leave the wingnuts in place. Repeat the measurements of P4 and P5. P7. For at least five different masses in turn, increase the mass (M) added to the crossbar from its initial value of 100 grams. Do not alter the distance (R) of the masses from the axis of rotation. For each choice of mass, repeat steps P4-P5. P8. Return the masses on the crossbar to their original values of 100 grams, but now change the distance R from the vertical shaft. Repeat steps P4-P6 for at least five different values of this distance. Note that P6 must be repeated each time R is changed, whereas it did not need to be repeated each time the loaded mass, M was changed in P7; why?mrQUESTION 1 The variables used in this experiment are m, M. r, R, h, and t. Match each of these variables with it's correct definition. * m A. length of the string AM B. distance from center of the crossbar to center of masses on either side c. height of the center of mass of the mass hanger above the floor, AR before the start of the motion D. hanging mass (including mass of hanger) E. mass on the hanger (mass of hanger not included) F. amount of mass placed on each side of the crossbar G. radius of vertical shaft, including the string that is initially wrapped around it H. total mass on the crossbar I. time of fall for the mass hanger j. height of bottom of the mass hanger above the floor before the start of the motion <. radius of the vertical shaft not including string l. crossbar question as part your analysis for this experiment you will need to derive equation moment inertia on page starting from an conservation mechanical energy. which following is correct energy situation odmghm variable v in mentioned previous sentence identified average translational velocity hanger it falls equal just before hits floor use lab manual calculate values different mass and position those masses variables i change a. both m r but all other remain same. changed only t changes. time fall be each configuration same throughout experiment. h because start heights amount s suppose measure diameter vetical cm hanging g. when place g either side a distance center obtain drop s. cm. remove wingnuts with no additional using derived one what value cm2 read instructions c1 carefully doing calculation. give answer two significant figures. theoretical placed axis rotation r-. based should expect slope log vs. graph b.2m oc.2 de.>