Newtonian mechanics - extended rigid body's rotation, moment of inertia

[puipui_queen]

Homework Statement

Figure shows the cylindrical skater, http://hk.geocities.com/puipui_queen/cylinder_skater.jpg [Broken]
as she spins,she may be modeled as a homogeneous cylinder of raduis R, height h, and density p, with outstretched arms. The arms are cylinders as welll, also of density p, radius r and length s. All these lengths are simple multiples of r.

Calculate the moment of inertia about the axis of cylindical body I_body, the moment of inertia of each outstretched arm I_out, and the moment of inertia of each arm when it is parallel to the axis of rotation, I_down, as shown in the figure.
2. Homework Equations

R=4r
h=36r
s=16r


3. The Attempt at a Solution

I_body = 1/2MR^2 = 4608p*pi*r
I_out, I tried using the eq'n 1/3ML^2, where L= s+R, but someone told me this is not right since it is the eq'n for thin rod, and the cylinder is not thin.

I_down, I am thinking about parallel axis theorm, where I = Icm + Md^2, and Icm = I_body and d = r+R, but then i don't think it is very logical... so I'm stuck...

And just wondering, there's more parts to this question, can I post the question under the same thread, or should I open a new thread for next part of the question.

 

[andrevdh]

... I_body = 1/2MR^2 = 4608p*pi*r ...

it should be r^5

For an outstretched arm:
The rotational inertia of a rod about an axis perpendicular to its length through its middle is

$$I_{rod} = \frac{1}{12}ML^2$$

about the skater's axis this will be an offset of

$$\frac{s}{2} + R$$