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rotational motion

# rotational motion - Laboratory Report PHYS122L Rotational...

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Unformatted text preview: Laboratory Report PHYS122L Rotational Motion Purpose of the Experiment: To apply Newton’s laws of motion to an analysis of a rotating disk. Specifically, to measure the moment of inertia of the disk, to measure the frictional torque acting on the disk, and to examine energy and angular momentum conservation in rotating systems. Experimental Procedure Throughout the experiment, a photogate and pulley will be used to directly measure the rotational speed of a disk. The photogate is connected to the computer through the LabPro interface and records data in the form of a plot of angular speed versus tim. Measuring I and τ f The rotational form of Newton’s second law states that the angular acceleration of a rotating system, d ϖ / dt, is proportional to the net torque τ net acting on the system: d ϖ / dt = τ net / I where ϖ is the angular velocity of the system and I is its moment of inertia. In this experiment, our rotating system is a disk that is acted upon by one or both of the following torques: 1) a frictional torque, τ f , which always acts in the opposite rotational sense to that of the angular velocity, ϖ 2) an applied torque, Tr o , which is produced by a string having tension T, attached to the disk at radius r o from the central axis. Case I: No string attached, only frictional torque acts: Two large disks are placed one on top of the other with the photogate/pulley sensor touching the lower disk. The pair of disks is given a moderate initial speed and the sensor is then used to record a plot of angular speed, ϖ , versus time. The slope of a five second interval of the early stages of the plot is found which can then be used to determine τ net / I . Case II: Both a string tension T and the frictional torque act simultaneously: A long string is attached to the topmost hole in the aluminum assembly that is on the top of the two disks. The string is cut so that a mass holder attached to the other end of the string is about 2 cm above the floor. A 100 g mass is placed on the holder and the string is wound around the aluminum until the mass is as high as it can go without coming in contact with the tabletop. The disk is held at rest in this position and data collection is started. The disk is allowed to rotate as the mass falls and a plot of d ϖ / dt is shown. ( d ϖ / dt ) falling and ( d ϖ / dt ) rising can then be calculated with the following equations: ( d ϖ / dt ) falling 2245 (+Mgr o- τ f ) / I and ( d ϖ / dt ) rising 2245 (-Mgr o- τ f ) / I The procedure is repeated four more times, adding 100 grams to the holder each time. There will be a total of 25 runs, five for each mass used. Energy considerations: All but 100 grams is removed from the holder and the mass is allowed to come to rest at its lowest point. The height of the holder above the floor is measured. This height will be used as the definition of H=0. The height H o of the mass at its highest position is then measured. The mass is allowed to fall from H o and produces a cyclic motion. The next six and produces a cyclic motion....
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rotational motion - Laboratory Report PHYS122L Rotational...

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