A physics student of mass 57.0 kg is standing at the edge of the flat roof of a building, 12.0 m above the sidewalk. An unfriendly dog is running across the roof toward her. Next to her is a large wheel mounted on a horizontal axle at its center. The wheel, used to lift objects from the ground to the roof, has a light crank attached to it and a light rope wrapped around it; the free end of the rope hangs over the edge of the roof. The student grabs the end of the rope and steps off the roof.
a) If the wheel has radius 0.300 m and a moment of inertia of 9.60 kg⋅m2 for rotation about the axle, how long does it take her to reach the sidewalk? Ignore friction.
b) How fast will she be moving just before she lands? (I have not done anything for part b yet)
I don't know if these are relevant, and I am sure I am missing some.
The Attempt at a Solution
As the person descends, there is a constant tension in the rope so the force acting on the person is
ΣF=ma=T-mg (Taking up as positive)
The height of the building is equal to the amount of rope required to descend, so the angle that the wheel must rotate through is
and so the angular velocity of the wheel is
But this is where is cannot figure out where to go from here.
I did try to solve this with energy, but it kept giving me an incorrect answer.
The moment of inertia does suggest energy method though, but I cannot get it to work properly.