encorelui2 said:Statics: If computing the moment of inertia about the y-axis of a triangular shape in the 2nd quadrant(not touching the x-axis); would i still use hb^3 /12
nvn said:encorelui2: So far, your formula looks correct. And, it is not limited to right triangles.
It does not matter whether it touches the x-axis or not. And it does not matter what quadrant it is in. It only needs to have one side coincident (collinear) with the y axis, assuming b is the horizontal width of your triangle.
Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is calculated by summing the products of each particle's mass and the square of its distance from the axis of rotation.
Moment of inertia is often compared to mass because they both involve the concept of inertia, but they are not the same thing. While mass is a measure of an object's resistance to changes in linear motion, moment of inertia is a measure of an object's resistance to changes in rotational motion.
The formula for calculating moment of inertia depends on the shape and distribution of an object's mass. For a point mass, the formula is I = mr², where m is the mass and r is the distance from the axis of rotation. For more complex objects, the formula is I = ∫r² dm, where r is the distance from the axis of rotation and dm is the infinitesimal mass element.
Moment of inertia plays a significant role in an object's rotational motion. The greater the moment of inertia, the more force is required to change an object's rotational speed. This means that objects with a larger moment of inertia will rotate more slowly than objects with a smaller moment of inertia when the same amount of force is applied.
Moment of inertia is an important concept in many fields, including physics, engineering, and biomechanics. It is used in designing structures and machines that rotate, such as bridges, wind turbines, and car engines. It also plays a role in understanding the movement and stability of objects in sports, such as figure skating and diving.