# Moment of Inertia and Radius of Gyration

**Moment of Inertia**

Moment of inertia, also called the second moment of area, is the product of area and the square of its moment arm about a reference axis.

Moment of inertia about the x-axis:

# 726 Area enclosed by parabola and straigh line | Centroid of Composite Area

**Problem 726**

Locate the centroid of the shaded area enclosed by the curve y^{2} = ax and the straight line shown in Fig. P-726. Hint: Observe that the curve y^{2} = ax relative to the y-axis is of the form y = kx^{2} with respect to the x-axis.

# 725 Centroid of windlift of airplane wing | Centroid of area

**Problem 725**

Repeat Problem 239 without using integration.

# 724 Rectangle, semicircle, quarter-circle, and triangle | Centroid of Composite Area

**Problem 724**

Find the coordinates of the centroid of the shaded area shown in Fig. P-724.

# 723 Rectangle, quarter circle and triangle | Centroid of Composite Area

**Problem 723**

Locate the centroid of the shaded area in Fig. P-723.

# 722 Semicircle and quarter circle | Centroid of composite area

**Problem 722**

Locate the centroid of the shaded area in Fig. P-722 created by cutting a semicircle of diameter r from a quarter circle of radius r.

# 721 Increasing the width of flange to lower the centroid of inverted T-beam

**Problem 721**

Refer again to Fig. P-714. To what value should the 6-in. width of

the flange be changed so that the centroid of the area is 2.5 in. above the base?

# 720 Two triangles | Centroid of Composite Area

Problem 720

The centroid of the sahded area in Fig. P-720 is required to lie on the y-axis. Determine the distance b that will fulfill this requirement.

# Three-digit numbers not divisible by 3

**Problem**

How many three-digit numbers are not divisible by 3?

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