Moment of Inertia of Right Angle Triangle about Centroid Axis

The moment of inertia of a right angle triangle about its centroid axis can be calculated using the parallel axis theorem.

Formula

The formula to calculate the moment of inertia of a right angle triangle about its centroid axis is given by:

I = (1/36) * b * h^3

Where,
I = Moment of inertia about centroid axis
b = Base of the triangle
h = Height of the triangle

Explanation

- The centroid of a right angle triangle is located at a distance of h/3 from the base and b/3 from the height.
- The moment of inertia of the right angle triangle is calculated with respect to the centroid axis, which is perpendicular to the base and passes through the centroid.
- Using the parallel axis theorem, the moment of inertia about the centroid axis can be calculated by adding the moment of inertia about the base axis (1/12 * b * h^3) and the product of the area of the triangle and the square of the distance between the base axis and the centroid axis ((1/6) * b * h * (h/3)^2).
- Simplifying the equation gives us the final formula for the moment of inertia of a right angle triangle about its centroid axis.

Therefore, the moment of inertia of a right angle triangle about its centroid axis is (1/36) * b * h^3.