- #1

bigevil

- 79

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## Homework Statement

A thin rod is 10 ft long and has a density which varies uniformly between 4 and 24 lb/ft. Find:

a) the mass

b) the x-coordinate of centroid

c) Moment of inertia about an axis perpendicular to the rod

d) Moment of inertia about an axis perpendicular to the rod passing thru the heavy end.

## The Attempt at a Solution

a) isn't difficult. I have got [tex]dm = (2x+4) dx[/tex], then integrate between 0 and 10 to get 140 lbs.

b) From [tex]\int \bar{x} dm = \int x dm[/tex], integrate and use earlier results to get 130/21.

c) I'm stuck at this one. I assume this means that the axis of MI passes through the centre of mass, so I set up the integration limits from 80/21 to -130/21 (rod is 10 foot). Then, taking [tex]I = \int x^2 dm = \int_{-130/21}^{80/21} 2x^3 + 4x^2 dx = 1.7(140) = 1.7m[/tex] (where m=140 lbs). But the answer (this question is from Mary L Boas' mathematical methods book) is 6.92m.

Am I missing something here? I am only calculating for the x-coordinate because the rod is "thin".