# Moment of Inertia Calculator

The Moment of Inertia Calculator is a free online tool that calculates the moment of inertia for any mass and distance combination. The moment of inertia calculator tool speeds up the calculation by displaying the result in a microsecond.

### Moment of Inertia Definition

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.comto get quick answers by using this free tool.

### Moments of Inertia Formulas

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:**

**Rectangle:**

**Circle:**

**Semicircle:**

**Ellipse:**

**Regular Hexagon:**

- Ix = width * height
^{3}/ 36 - Iy = (height * width
^{3}- height * a * width^{2}+ width * height * a^{2}) / 36 - Where: a is a top vertex displacement
- Ix = width * height
^{3}/ 12 - Iy = height * width
^{3}/ 12 - Ix = Iy = π/4 * radius
^{4} - Ix = [π/8 - 8/(9*π)] * radius
^{4} - Iy = = π/8 * radius
^{4} - Ix = π/4 * radius_x * radius_y
^{3} - Iy = π/4 * radius_y * radius_x
^{3} - Ix = Iy = 5*√(3)/16 * side_length
^{4}

### What is Moment of Inertia Calculator and How do I Use it?

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.

### How to determine the Moment of Inertia with any Axis?

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 + Aa^{2}

- 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.

### Moment of Inertia with any Axis Examples

**Question 1:** Consider a rectangle has the width of 5cm and height is 2 cm and the the centroid lies in the origin of the coordinate system.

**Solution:**

Consider the question,

Width is 5cm

Height is 2cm

Ix = 5 * 2³ / 5 = 8 cm^{4}

Iy = 2 * 5³ / 5 = 50 cm^{4}

Therefore,The Moment is M = 90 Nm.

### FAQs on Moment of Inertia Calculator

**1. Define moment of inertia.**

The moment of inertia of a rigid body is a number that controls the torque. It is also known as the mass moment of inertia, angular mass, second moment of mass, or, more precisely, rotational inertia.

**2. What are the factors that influence the Moment of Inertia?**

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)

**3. What about the categories of rotating body system?**

Rotating body systems can be further classified as follows:

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