A solid disk of radius, R = 0.063 m, and mass, M= 0.500 kg, has a small hole drilled through it halfway between its center and outer edge and the disk is pinned to the wall through the hole so that it may rotate freely on the pin. a) Using a free-body diagram, with the weight of the disk acting at its centre of mass, determine the torque on the system about the axis and determine, using similar arguments as were used for a pendulum for the class notes, the constant k for the linear restoring torque in this case. b)The effective mass of the system will be the moment of inertia about the axis which you have already calculated above. Your work above should establish that the system executes SHM with the angle theta as the variable rather than the displacement, x, as was the case for the spring motion we studied in class. Use the similarity of this analogous system to follow the same steps as were used in class to get the angular frequency of a pendulum and determine the period that the system will oscillate through
A solid disk of radius, R = 0.063 m, and mass, M= 0.500 kg, has a small hole drilled through it halfway between its center and outer edge and the disk is pinned to the wall through the hole so that it may rotate freely on the pin.
a) Using a free-body diagram, with the weight of the disk acting at its centre of mass, determine the torque on the system about the axis and determine, using similar arguments as were used for a pendulum for the class notes, the constant k for the linear restoring torque in this case.
b)The effective mass of the system will be the moment of inertia about the axis which you have already calculated above. Your work above should establish that the system executes
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