# Radius of Gyration

## Area, moment of inertia, and radius of gyration of parabolic section

**Situation**

Given the parabola 3x^{2} + 40y – 4800 = 0.

Part 1: What is the area bounded by the parabola and the X-axis?

A. 6 200 unit^{2}

B. 8 300 unit^{2}

C. 5 600 unit^{2}

D. 6 400 unit^{2}

Part 2: What is the moment of inertia, about the X-axis, of the area bounded by the parabola and the X-axis?

A. 15 045 000 unit^{4}

B. 18 362 000 unit^{4}

C. 11 100 000 unit^{4}

D. 21 065 000 unit^{4}

Part 3: What is the radius of gyration, about the X-axis, of the area bounded by the parabola and the X-axis?

A. 57.4 units

B. 63.5 units

C. 47.5 units

D. 75.6 units

## 818 Hollow square section | Moment of Inertia and Radius of Gyration

**Problem 818**

A hollow square cross section consists of an 8 in. by 8 in. square from which is subtracted a concentrically placed square 4 in. by 4 in. Find the polar moment of inertia and the polar radius of gyration with respect to a z axis passing through one of the outside corners.

## 817 Hollow Tube | Moment of Inertia and Radius of Gyration

**Problem 817**

Determine the moment of inertia and radius of gyration with respect to a polar centroidal axis of the cross section of a hollow tube whose outside diameter is 6 in. and inside diameter is 4 in.

## 816 Polar moment of inertia and radius of gyration at one corner of rectangle

**Problem 816**

A rectangle is 3 in. by 6 in. Determine the polar moment of inertia and the radius of gyration with respect to a polar axis through one corner.

## 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: