Calculate the radius of gyration of the x component of a triangle with base of 360mm and height 180mm if the triangle is located on the x and y axis

Mathematics
1

calculate the radius of gyration of the x component of a triangle with base of 360mm and height 180mm if the triangle is located on the x and y axis.

2

calculate the radius of gyration of the x component of a triangle with base of 360mm and height 180mm if the triangle is located on the x and y axis.

answer: The radius of gyration of a 2D body is given by the formula:

kx = sqrt(Ix / A)

where kx is the radius of gyration of the x component, Ix is the moment of inertia of the x component, and A is the area of the triangle.

The moment of inertia of a triangle with respect to its centroid is given by the formula:

Ix = (b * h^3) / 36

where b is the base of the triangle and h is its height.

The area of the triangle is given by the formula:

A = (b * h) / 2

Substituting these values, we get:

Ix = (360mm * (180mm)^3) / 36
= 58320000 mm^4

A = (360mm * 180mm) / 2
= 32400 mm^2

So,

kx = sqrt(Ix / A)
= sqrt(58320000 mm^4 / 32400 mm^2)
= 480.62 mm

Therefore, the radius of gyration of the x component of the triangle is approximately 480.62 mm.