Item $3$

Learning Goal:

To be able to determine a simple areats radius of gyration

In structural mechanics, an areats radius of gyration about an axis is a quantity that is often used in the design of columns. Provided that the areas and moments of inertia are known. the radii of oviation are determined from the following formulas

$k_2=\sqrt[\phantom{2}]{\frac{L_x}{A}}$

$k_y=\sqrt[\phantom{2}]{\frac{t_y}{A}}$

$k_0=\sqrt[\phantom{2}]{\frac{J_0}{A}}$

where $L_z$ is the area's moment of inertia about the $x$ axis, $I_y$ is the area's moment of inertia about the $y$ axis, $J_0$ is the petar moment of inerta, and $A$ is the area.

Figure

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Part A

Which, if any, of the following choices are the correct units for the radius of gyration?

Check all that apply.

$f{t}^2$

$m^4$

$m^2$

$m^3$

m

$f{t}^4$

ft

$f{t}^3$

$$ Request Answer

X Incorrect; Iry Again

Part B

As shown, a triangle has a base of $b=7\mathrm{.}70ft$ and a height of $h=1\mathrm{.}60ft.($Figure $1)$ What is $k_z,$ the triangle's radius of gyration about the x axis?

Express your answer numerically to three significant figures and include the appropriate units

Part C

What is $ko,$ the polar radius of gyration of a circle of radius $r=4\mathrm{.}20ft,$ when the pole is a point $O$ on the circumference of the circle? $($Figure $2)$

Express your answer numerically to three significant figures and include the appropriate units.

View Available Hint$($s$)$

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Part D Express your answer numerically to three significant figures and include ththe appropriate units$][$