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course PHY 201
5/2 about 7:05 pm
I viewed this experiment and it allowed me to answer the question in Query 32.Experiment 30. When a change in the angular velocity of a disk is the result of a changing gravitational or elastic potential energy, the change in the total kinetic energy of the rotating disk is equal and opposite to the potential energy change.
Associated video clip is on the CD EPS02.
Steel bolts are embedded in a Styrofoam disk, forming rings with varying numbers of bolts and various radii. The disk is constrained to rotate about horizontal axle.
By allowing a weight attached a thread wound around the horizontal axle of the disk to fall through a known distance, with the entire system initially a rest, the time required for the weight to fall permits us to determine the average velocity of the weight and to infer, from the presumed uniform acceleration, its final velocity. From this final velocity and the radius of the axle the final angular velocity of the disk can be inferred. From the velocities of the various bolts, and hence their kinetic energies, can be determined. The potential energy loss of the falling weight, the total kinetic energy of the bolts and the (negligible) kinetic energy of the falling weight can then be compared.
The relationship between the torque exerted by the falling weight, the total of the mr^2 contributions of the bolts, and the angular acceleration of the system can be determined, with the conclusion that the angular acceleration is equal to the torque divided by the total of the mr^2 contributions. This leads to the definition of moment of inertia.
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Very good.
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