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'Net Torque = I alpha' applied to a cylinder descending as it unwraps a cord from its surface.

A cord is wrapped on the surface of a uniform cylinder, of mass M=12 kg and radius R= .36 m. Released from rest with the cord vertically tangential to its surface and tied to a ceiling support, the cylinder descends with angular acceleration A as the cord unwinds from its surface.
SEE ATTACHMENT FOR PICTURE OF APPARATUS.
a. Find the angular acceleration as the cylinder descends.
b. Find the distance, D, the c.m. descends in the first 2.4 seconds.

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Note; since the force exerted by the cord and the force of gravity are both vertical, the cord remains vertical as the cylinder descends.
a. For an axis at the c.m. of the cylinder, applying 'net force = Io A', in terms of cord force C, angular acceleration A, and the moment ...

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