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WY

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A block of mass m is attached (with a massless string) to a wheel. Consider the bicycle wheel is not turning initially. The block is allowed to fall a distance of h. Assume that the wheel has a moment of inertia I about its rotation axis.

Find the angular speed of the wheel after the block has fallen a distance of h in terms of m,g,h, r(of the wheel) and I

I took the relative zero as where the mass is starting from:

so the wheel has KE = 0 and the mass has KE=0 and PE=0

Then after it has fallen a height of h:

Wheel: KE = 1/2(I*omega^2)

Mass: KE = 1/2mv^2 and PE=mgh

so i came up with the conservation of energy equation to be:

0 = 1/2(I*omega^2) + 1/2mv^2 + mgh

the v the weight will be traveling at will be the same angular velocity the wheel is turning i substituted omega in for v

the I rearranged it so that omega was the subject and got:

omega = sqrt((-2mgh)/(Im))

is this rite? or ami completely wrong?? thanks in advance :)