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A 4.00 m length of light nylon cord is wound around a uniform cylindrical spool of...

A 4.00 m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.00 kg. The spool is mounted on a frictionless axle and is initially at rest. The cord is pulled from the spool with a constant acceleration of magnitude 2.90 m/s2. How much work has been done on the spool when it reaches an angular speed of 7.30 rad/s? (The answer is not 0.9125 J)

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Answer #1

Moment of Inertia of cyclindrical spool,
I = 0.5*m*r^2
= 0.5*1*(0.5)^2
=0.125 Kg.m^2

w = change in rotational kinetic energy
= 0.5*I*wf^2
= 0.5*(0.125)*(7.3)^2
= 3.331 J

Answer: 3.331 J

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