(adsbygoogle = window.adsbygoogle || []).push({}); A circular disk having a radius of 4ft. and weighing 40lb. has a small weight of 20 lb attached to it at a distance of 2ft. from its center. If the disk is in the vertical plane and set in rotation about an axis through its center so that its minimum speed is 120 rpm, find its maximum speed.

For this problem I'm pretty sure I need to use equations such as

ω=dθ/dt, α=dω/dt, and most likely α=ω(dω/dθ)

On my first try I was trying to avoid using the derivative equations. I know the minimum will be at the top, and the maximum at the bottom of the wheel. So in the first attempt I solved for the work done by the 20lb weight using -(ΔV), and equating that to the change in kinetic energy of the wheel. My solution was 121.068rpm, but that seems to simple, and frankly wrong.

What I realize is that the 20lb weight is applying a torque to the wheel, so I likely need to integrate over that torque to understand the change in the angular momentum to finally solve for ω when the point has gone ∏rads through a rotation from the minimum value, 120, at the top

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# Non-uniformly accelerated rotation

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