∫∫∫dydxCarnivroar said:
The moment of inertia of a triangle rotated about the y-axis is a measure of its resistance to rotational motion around this axis. It is denoted by the symbol Iy and is calculated by multiplying the mass of the triangle by the square of its distance from the y-axis.
The moment of inertia of a triangle rotated about the y-axis is different from that of a rectangle because of their different shapes. While a rectangle has a constant moment of inertia regardless of its orientation, the moment of inertia of a triangle varies depending on its rotation due to its uneven distribution of mass.
The moment of inertia of a triangle rotated about the y-axis can be calculated using the formula Iy = (1/36) x m x h2 x (a2 + 4b2), where m is the mass of the triangle, h is the distance from the y-axis to the base of the triangle, and a and b are the dimensions of the triangle's base and height, respectively.
The position of the triangle's centroid, which is the point where all its mass is concentrated, affects its moment of inertia when rotated about the y-axis. The further the centroid is from the axis of rotation, the higher the moment of inertia will be, and vice versa.
No, the moment of inertia of a triangle rotated about the y-axis cannot be negative. It is always a positive value since it represents the resistance to rotation, and rotation is always a positive/angular motion.