Moment of Inertia Problem?

Question

A fishing line of length 4 m is wrapped around the axle of a wheel. The axle's diameter is 4 cm. One end of the line is attached to a mass of 6 kg. When the mass is released, gravity pulls on it and this causes the axle to rotate. When the line has been completely unwound from the axle, the wheel is rotating at an angular speed of 3 rev/sec. Calculate the moment of inertia of the wheel and axle.

My answer comes out to 1.322 kg m^2/rad^2.

Am I correct? Thanks.

Answer 1

First step is to calculate the angular displacement
the circumference if the axle is
.04*3.14
and 4 m is
31.85 radians
therefore


31.85=.5*α*t^2

3 rev/sec is 6*3.14 rad/sec
18.84 rad/sec
therefore
18.84=α*t

combine and solve for α

31.85=.5*18.84*t

t=3.38

α=5.57

6*9.81*.02=I*α
therefore
I=0.21

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