# Moment of Inertia for three rods

1. Dec 6, 2004

### hL

1. Three rods, each of length L and mass M, are welded together perpendicularly (like an x-y-z coordinate system). The axis of rotation is drawn in pink in the image below. I have to find the moment of inertia.

I used the parallel-axis theorem to get:
I = I-cm + MD²
I = 2(.5ML²) + M(L/2)²
I = (5/4)ML²

I'm not sure if I'm right, could someone check my method?

2. Picture 2 is a car tire. It has two sidewalls (gray) of uniform thickness 0.635 cm and a tread wall (cyan) of uniform thickness 2.5 cm and width 20.0 cm. Its density is uniform, with a value of 1.10E3 kg. Find its moment of inertia about an axis through its center, perpendicular to the plane of the sidewalls. (A = 16.5 cm, B = 30.5 cm, C = 33.0 cm).

I have no idea what to do.

3. What values would you need to estimate the moment of inertia of your body as you stand tall and turn in a vertical axis passing through the top of your head to the point between your feet?

Again, I have no idea what to do.

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Last edited: Dec 6, 2004
2. Dec 6, 2004

### Sirus

For all three problems, you need to split objects of compound shapes (i.e. of shapes compiled from many simpler shapes) into their familiar parts, of which you know the equations for moment of inertia. For #1, you must find the moment of inertia of each rod with respect to the axis of rotation, then add them together. For #2, what familiar shapes make up the tire? For #3, what shape is similar to the human body?