18600 Angular Momentum

Transcription

1 18600 Angular Momentum

2 Experiment 1 - Collisions Involving Rotation Setup: Place the kit contents on a laboratory bench or table. Refer to Figure 1, Section A. Tip the angular momentum apparatus base on its side. Turn the adjustable thumbscrews located at each corner of the base until the screws protrude about ½" through the bottom of the base. Press each of the protective caps firmly onto the bottom of the thumbscrews. Unscrew each thumbscrew until the caps are flush with the bottom surface of the base. Tighten the lock nuts with an adjustable open end wrench. Refer to Figure 1, Section B. With the apparatus base still on its side, remove the nuts from the three carriage bolts on the base. Completely remove one of the three carriage bolts and slightly raise the heads of the remaining two. Insert the flanged spindle of the rotating base disc. Replace the third carriage bolt and the nuts. Tighten evenly and make sure the spindle is centered and perpendicular to the base. Return the apparatus base to its upright position. Figure 1 Use a spirit level to determine if the rotating base disc is level. Adjust the leveling thumbscrews in the angular momentum apparatus base as necessary to level the disc. Put the e" dowels in the two holes in the front of the apparatus base. Anchor the base by placing C-clamps so they engage the tops of the dowels and the underside of the lab bench or table. Check the level again, and make adjustments as necessary. Refer to Figure 1, Section C. Remove the washer from under the tape on the moveable arm. Place the drilled end of the arm over the center axle of the rotating base disc, making sure to align the other hole in the arm with the pre-drilled hole in the base disc. Place the washer over the end of the axle. Thread the extension collar over the axle, and tighten by hand to hold the arm in place. Insert the sheet metal screw through the other hole in the moveable arm, and screw down into the hole provided in the base disc. Select the 2" aluminum rod and insert it into the drilled hole in the extension collar. Use it as a wrench to tighten the extension collar securely. (The 2" rod can also be used to remove the steel balls from the

3 rubber cups). Recheck the level of the rotating base disc. Note that the moveable arm will not drift by itself if the rotating base disc is level. Refer to Figure 2. Select the ramp support. Center the pre-drilled hole in the ramp support over the far left threaded bolt on the left end of the angular momentum apparatus base. Line up the short end of the ramp support base parallel to the front of the apparatus base. Remove the flanged wing nut from the neighboring center bolt, and use it to secure the ramp support to the apparatus base. when released from the top of the ramp. Figure 2 Refer to Figure 3. Remove the flanged wing nut and bolt from the upright part of the ramp support, and attach the aluminum ramp. Tighten the wing nut, making certain that the sides of the ramp support are flush with the ramp. Align the end of the ramp with the rubber cup on the end of the moveable arm. Make any necessary adjustments to assure the rubber cup will receive a steel ball The apparatus is now ready for use in this experiment. Operating the pre-installed timer Mechanism: Install a fresh C flashlight cell in the battery holder on the angular momentum apparatus base. Use a piece of masking tape to attach a strip of the recording tape to the circumference of the rotating base disc.

4 (If made long enough, the masking tape piece can also be attached to the top surface of the rotating base disc and used as a rotation marker). Place the lap in the recording tape slightly to the left of the timer when the rubber cup on the end of the moveable arm is aligned with the end of the aluminum ramp. This will ensure that the lap does not interfere with the recording during this experiment. Make sure the carbon side of the timer s carbon disc is facing the recording tape. Check the carbon disc to see that it is loosely retained by a small thumbtack pushed into the prepared hole in its rubber mount. When loosely retained, the carbon disc is free to rotate when the timer is running, and the timer will make clear marks on the recording tape. Note that the wing nut spring suspension of the timer mechanism can be released to make carbon disc adjustments. Slide the timer recording head vertically to the recording position so the bead will strike the recording tape. The impact of the bead on the tape can be adjusted using the horizontal thumbscrew in the timer mechanism. Set it so the bead is hitting the tape just hard enough to leave a clear mark. The timer runs as long as the push button is held down. (Note: Start the timer when the steel ball is released from the top of the ramp). It is advisable to use the first piece of paper tape for making adjustments. Replace it to take data. (Notice that the wing nut spring suspension of the timer mechanism can be adjusted vertically to make several recordings on a single strip of recording paper). Procedure: A steel ball released from the top of the ramp will have a certain kinetic energy when it reaches the bottom and hits a rubber cup on the movable arm. Will the recoil speed of the arm and the disc to which it is attached depend upon which of the cups is hit? Since different points on the arm move at different speeds, it is convenient to use the speed of the disc s rim as a measure of the recoil speed. The ramp can be placed at three different distances from the center of the disc so that the ball is caught in each of the three cups in turn. In order to assure that you end up each time with exactly the same object after the collision, place two steel balls in the rubber cups which are not in use at the moment. Then, three balls will always be in the arm attached to the disc after the collision. Before you start your measurements, be sure the rotating base disc is level. Make several trials for each of the three positions of the ramp, having a partner record each trial with the timer. Always start the ball from the top of the ramp. How do the ratios of the rim speeds compare with the ratios of the distances from the center of the disc to the points of impact?

5 The rubber cup on the end of the moveable arm and the aluminum ramp can be adjusted to change the angle of impact of the ball. Investigate the rim speed as a function of the angle of impact. (Note: The ramp support must be removed from any of the three threaded bolts and held in place by hand for this investigation). Which trigonometric function describes this dependence? Experiment 2 - Moment of Inertia Setup: Use the 2" aluminum rod to loosen and remove the extension collar. Remove the washer and screw holding the moveable arm to the rotating base disc, and lift off the moveable arm. Remove the ramp support. Replace the extension collar over the axle on the base disc. Tighten the extension collar securely with the 2" aluminum rod. Attach a new strip of recording tape to the rotating base disc. Procedure: The moment of inertia of a homogeneous rigid body depends on its mass, its shape, and the location of the axis of rotation. In this experiment, you will investigate the dependence of the moment of inertia on the shape of the body by making collisions between different rotating objects of approximately the same mass and the same largest linear dimension. The rim speed of the base disc can be measured directly in centimeters per mark by using the same recording tape timer setup described in the previous experiment. Can you use the same data to represent the angular velocity of the disc? 1. Before taking measurements, be sure that the rotating base disc is level and free to rotate. Spin the rotating base disc, hold the 10" diameter drop-on wood disc above it, and drop it as a partner records the angular velocity before, during, and after the collision. To prevent the marks on the recording tape from overlapping, your partner should operate the timer for less than one revolution during this experiment. Plot the angular velocity as a function of time. (Note: The two discs are of nearly equal mass and diameter). Is the angular velocity constant before and after the collision? You may find that the duration of the collision is long enough for the friction to introduce significant errors in the determination of the

6 angular velocity before and after the collision. How can you use your graph to reduce the error? Repeat the experiment with different initial angular velocities. Is the total angular momentum conserved in the collision? The two discs have equal radii, but be sure to weigh them before you propose that they have the same mass. If you find that the masses are different, how does this affect your expression for the angular momentum after the collision? Repeat the experiment with the dumbbell weight set. Notice on the set that the distance from the middle of the aluminum bar to the center of each cylinder equals the radius of the disc. How does the moment of inertia of a disc of the same mass and radius compare? (Again, correct for any discrepancy in the mass). Can you ignore the contribution of the aluminum bar to the total moment of inertia? On what do you base your answer? How does the moment of inertia of the rectangular block compare with that of the two metal cylinders of equal mass when the distance between their centers of mass equals the length of the block? Knowing the masses of the disc, arm, and steel balls used in the previous experiment, guess the moment of inertia of the whole assembly. Calculate and compare the results. Experiment 3 - Changing Angular Momentum Setup: Refer to Figure 4. Place the concentric disc set over the extension collar. With the steel cylinder weights facing upward, align the hole in the center of the dumbbell weights with the hole in the center of the concentric discs. Thread the wing screw through the center hole of the dumbbell weights and the concentric disc set. Tighten the entire assembly. Attach a new strip of recording tape to the rotating base disc. Wrap several turns of recording tape around the smallest diameter disc in the disc set. Tape or hook the free end of the recording tape to the

7 end of the constant force puller (the dowel with a rubber band attached). When the metal hook is pulled by hand to a specific mark on the dowel, and this position is maintained, a constant and repeatable force is applied to the paper tape. Make a specific mark on the dowel with a pencil, and use it as a reference for applying a constant force. You may want to practice maintaining this position before taking data. Procedure: You know from experience that when you make a door swing, its motion depends not only on how hard you push but also on where you push. In this experiment, you will study quantitatively the changes in the angular momentum produced by a non-central force acting at a distance from the axis of rotation. As you pull the free end of the paper tape with a constant force, have a partner record the disc rotation rate (again, for less than one revolution to prevent the marks from overlapping). Make several runs for each diameter on the stack of concentric discs, recording each trial. Plot the average rim speed over, say, every five tick interval as a function of time. Is the rate of change of angular momentum constant in each run? How does the rate of change of angular momentum depend on the distance between the axis and the point at which you apply the force? How must you change the force if you want to apply it at the inner and then at the middle disc, and still end up with the same rate of change of angular momentum? Try it. What is the relevant quantity that determines the rate of change of angular momentum for a given object rotating around a fixed axis? With several turns of recording tape wrapped around one of the concentric discs, start from rest, and pull the tape a fixed distance with a constant force. How do you predict the final angular velocities will compare when you apply the force at each of the three concentric discs? Try it. If you have a stopwatch, compare the times required to pull the tape in the three cases. Can you think of a similar situation in motion on a straight line? Adjustments in the Apparatus for use with a Photoelectric Acceleration Timer: Data can be recorded using a photoelectric timer instead of the mechanical timer mounted on the apparatus base. To use such a timer, place the dowel insert of the rectangular wooden timer post into the hole in the base next to the battery holder. Use a C-clamp to attach the timer to the post. Follow the instructions that accompany the timer.