Radius of Gyration

Consider the cross-section below. A compressive load P is applied at any point (e_x, e_y) with respect to the principal axes x and y. The moment of P about these axes are respectively
 

Situation
Given the parabola 3x² + 40y – 4800 = 0.
 

Part 1: What is the area bounded by the parabola and the X-axis?
A. 6 200 unit²
B. 8 300 unit²
C. 5 600 unit²
D. 6 400 unit²
 

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 unit⁴
B. 18 362 000 unit⁴
C. 11 100 000 unit⁴
D. 21 065 000 unit⁴
 

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
 

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.
 

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.
 

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
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: