Given: m = 0.25 kg = mass of cylinder l = 0.108 m = length of cylinder d = 0.063

Question

Given:

m = 0.25 kg = mass of cylinder
l = 0.108 m = length of cylinder
d = 0.0638 m = diameter of cylinder

Asked:

I = moment of inertia = ?

Energy conservation:

The cylinder has no initial kinetic energy, but it has potentialenergy.
Ei = Ui = mgh, h = L*sinq =3m*sin(25o)

The cylinder has no final potential energy, but it hastranslational and rotational kinetic energy.

Ef = Kf = ½ mv2 +½ Iw2. Here v and w are the final speed andangular speed, respectively.
Ei = Ef (energy conservation)

mgh = ½ mv2 + ½ Iw2. For rolling w and v are related, w = v/r = 2v/d.
We therefore have
mgh = ½ mv2 + 2Iv2/d2.
This equation contains 2 unknowns, I and v. We need to find vto be able to solve for I.
vavg = distance traveled/time = L/Dt.
But we also have vavg = (vi +vf)/2= vf/2 = v/2, since vi = 0.
Therefore v = 2L/Dt.
No we can solve for I in terms of all known quantities.
I = (mgh - ½mv2)d2/(2v2)

Explanation / Answer

you're right, answer: C

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