What is the angular acceleration of the flywheel?

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Radius of flywheel=r=0.600/2=0.300 m

The flywheel starts from rest, and 5.00 m of rope are unwound in 2.00 s.

initial angular velocity=wi=zero

angular displacement=theta(O)=distance/radius

angular displacement=theta(O)=5/0.3=16.666 radian

angular acceleration= alpha=a!

theta(O)=[1/2 ]a!*t^2

angular acceleration= a!= 2*O / t^2

angular acceleration= a!=2*16.66/4=8.333 rad /s^2

A) The angular acceleration of the flywheel is 8.333  rad/s^2
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final angular speed=wf=?

wf=wi+a!t

but wi = 0

wf =a1T=8.333*2=16.666  rad/s

B) final angular speed is16.666 rad/s
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 Final kinetic energy  =KE=work=force*distance=40*5=200 J

C)  Final kinetic energy is 200 J
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Kinetic energy=KE=(1/2)I*wf^2

moment of inertia about the rotation axis=I=2KE/wf^2

D) Moment of inertia about the rotation axis=2*200 /(16.666)^2=1.4401 kgm^2

moment of inertia about the rotation axis is 1.4401 kgm^2
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