Estimate the properties listed below for the area shown. Your estimates should be in the ballpark of the actual values. Estimates should take less

than a few minutes to determine and take minimal calculations.

Area

Centroid

The radius of Gyration about the $y-$axis

The radius of Gyration about the $x$ axis

Moment of Inertia about the $y-$axis

Moment of Inertia about the x$-$axis

Polar Moment of Inertia

Hint: The radius of gyration will be slightly further from the rotation axis than the

centroid

Hint: Moment of Inertia $=($ Radius $of$ Gyration ${)}^2$ times Area

The illustrations at GeoGebra $G$ may be useful for approximating the radius of gyration and then the moment of inertia.

Part $2$

Estimate the load in the hooks and chains supporting the light fixture.

The pine beam is a $42$ in$.$ long $6$ by $8(5\mathrm{.}5$ in$.$ by $7\mathrm{.}5$ in$.)$

for the density of wood is Oregon Pine $530$ kg$/$m$^3$ and steel is $7850$ kg$/$m$^3$