Moment of Inertia Calculator

The angular mass of the object is to describe the moment of inertia. It is defined as the rotating object's inertia with regard to rotation. In other words, it is described as an object's proclivity to stay in a condition of rest or motion. The moment of inertia is used to calculate body movement. There is a distinction between inertia and inertia moment.

In linear motion, the moment of inertia serves the same purpose as mass. It's a measurement of a body's resistance to a change in rotational motion. It is constant for a rigid frame with a defined rotational axis.

The following things influence the moment of inertia:

• The material's density
• The body's shape and size
• Rotational axis (distribution of mass relative to the axis)

Rotating body systems can be further classified as follows:

• Discrete (System of particles)
• Consistent Continuous(Rigid body)

For more concepts check out physicscalculatorpro.com to get quick answers by using this free tool.

Finding the second instant of area of any arbitrary form usually requires integration. However, for the most frequent shapes, you can use the formulae below.

Remember that these formulas are only true if the coordinate system's origin and the area's centroid are the same. In other words, these equations hold if both the x- and y-axes cross the centroid of the examined shape.

Triangle:

• Ix = width * height³ / 36
• Iy = (height * width³ - height * a * width² + width * height * a²) / 36
• Where: a is a top vertex displacement

Rectangle:

• Ix = width * height³ / 12
• Iy = height * width³ / 12

Circle:

• Ix = Iy = π/4 * radius⁴

Semicircle:

• Ix = [π/8 - 8/(9*π)] * radius⁴
• Iy = = π/8 * radius⁴

Ellipse:

• Ix = π/4 * radius_x * radius_y³
• Iy = π/4 * radius_y * radius_x³

Regular Hexagon:

• Ix = Iy = 5*√(3)/16 * side_length⁴

The following is how to use the moment of inertia calculator:

• Fill in the values of mass and distance in the appropriate input fields.
• To get the answer, click the calculate button.
• Finally, in the output field, the moment of inertia will be shown.

What about if the coordinate system's origin isn't the same as the centroid? Do not really worry, the second moment of the region can still be discovered! The parallel axes theorem must be applied. Let's imagine you wish to find the area moment around an axis that is parallel to the x-axis but in the distancea. You can use the formula: I = Ix + Aa²

• Here, I be the moment of inertia about the axis parallel to the x-axis,
• Ix be the moment of inertia about the x-axis,
• A denotes the area
• a be the distance between two parallel axes.