Chapter 5.3, Problem 6P

The following notation is used in the problems: $M\text{ = mass}$, $\bar{x},\bar{y},\bar{z}=$ coordinates of center of mass (or centroid if the density is constant), $I=$ moment of inertia (about axis stated), $I_x,I_y,I_z=$ moments of inertia about x, y, z axes, $I_m=$ moment of inertia (about axis stated) through the center of mass.

Note: It is customary to give answers for $I,I_m,I_x$, etc., as multiples of M (for example, $I=\frac{1}{3}M{l}^2$).

A triangular lamina has vertices (0, 0), (0, 6) and (6, 0), and uniform density. Find:

(a) $\bar{x},\bar{y}$,

(b) $I_x$,

(c) $I_m$ about an axis parallel to the x axis. Hint: Use Problem 1 carefully