How Does Mass and Height Affect the Angular Speed of a Rotating Bicycle Wheel?

[PascalPanther]

"Consider the bicycle wheel is not turning initially. A block of mass m is attached (with a massless string) to a wheel. 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"

This is what I did:

U + K + W(other) = U + K
mgh + 0 + 0 = 0 + 1/2mv^2 + 1/2 I*omega^2

omega = Sqrt[(2mgh - mv^2)/I]

This is wrong... what am I doing wrong? I know I can use omega = v^2/r, but not sure where that would go...

 

[OlderDan]

"Consider the bicycle wheel is not turning initially. A block of mass m is attached (with a massless string) to a wheel. 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"

This is what I did:

U + K + W(other) = U + K
mgh + 0 + 0 = 0 + 1/2mv^2 + 1/2 I*omega^2

omega = Sqrt[(2mgh - mv^2)/I]

This is wrong... what am I doing wrong? I know I can use omega = v^2/r, but not sure where that would go...

ω = v^2/r is not correct, but it is sort of close. When you get it right, you can replace either v or ω using the correct relationship. Since you want to solve for ω, replace the v and solve away.