Homework Help: Tire/moment of Inertia

1. Jan 27, 2005

bemigh

Hey,
Im having a lot of difficulty with this certain problem...

The rubber tire has two sidewalls of uniform thickness 0.688 cm and a tread wall of uniform thickness 2.60 cm and width 21.1 cm. Assume that L1=17.9 cm, L2=29.0 cm and L3=31.6 cm. Suppose its density is uniform, with the value 1.09×103 kg/m3. Calculate its moment of inertia about an axis through its center perpendicular to the plane of the sidewalls.

The image provided has L1 showing the radius of the rim, L2 being the radius from the center of the rim to the inner edge of the tread, and L3 from the radius from the center of the rim to the outer edge of the tread. ive already used many guesses, because i thought i could find the volume of the tire, then use it to find the mass of the tire, thus calculating the moment of Inertia using the radius of the tire, but it still didnt work... any ideas or clarifications would be awesome,
Cheers

2. Jan 28, 2005

oldunion

not sure what you specifically mean by rim. but this is what i would do: find volume of whole tire as if it were a solid disc, subtract volume of center disc where the wheel would go, then subtract volume of tire from volume of tire without wheel volume. so mathematically like this:
a=whole disc
b=wheel space
c=whole tire

a-b=c

once you have c then you can find the volume of that whole tire minus the hollow space denoted: c-d where d is the volume of the tire with the hollow air space taken into account. this will give you the volume of the tire.

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