A solid cylinder (mass 10 kg and radius 10cm) is mounted so it is free to rotate

Question

A solid cylinder (mass 10 kg and radius 10cm) is mounted so it is free to rotate about a fixed horizontal axle that passes through the centers of its circular ends. A block is hung from a cord wrapped around the cylinder's circumference. When the block is released the cord unwinds and the block accelerates downward. The tension in the string is 2.3N during this time and the string is always tangent to the circle as the block falls. There is no friction between the cylinder and the axle
1) If it takes 5 seconds for the string to completely unwind from around the cylinder determine the number of revolutions the cylinder turns through during this time.
2) How long is the string?

Explanation / Answer

torque=2.3*r=0.23 units
torque=I

=1.15rad/sec^2

using

=1/2t^2

=14.375 rad

no of rev=2.28

length=14.375*10^-1=1.43m

:)

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