# Mass Moment of Inertia Calculator

The Mass Moment of Inertia Calculator is a real-time online tool that calculates the moment of inertia of objects of various shapes by simply entering the information into the fields. After entering the mass and distance, press the calculate button to get the results in less time.

Mass Moment of Inertia Calculator: If you want to solve mass moments of inertia problems quickly, then our free online Mass Moment of Inertia Calculator is the way to go. In the sections below, you may learn more about what the moment of inertia is and how to calculate it using formulas. Get a step-by-step guide on calculating the moment of inertia of an object, as well as answers to sample questions.

## What is the Moment of Inertia?

The rotational inertia of a body is measured in moments of inertia relative to a defined, fixed axis of rotation. It calculates the torque required to achieve the desired angular acceleration. It's the same way that mass determines the force required to achieve the desired acceleration. To put it another way, the moment of inertia describes how difficult it is to rotate an item along a given axis. The kilogramme square is the SI unit for the moment of inertia.

### Moment of Inertia Formula

The formulas for the moment of inertia for various shapes are listed below

• Moment of Inertia of a ball I = (2/5)mr²
• Moment of Inertia of circular hoop I = mr²
• Cuboid Moment of Inertia I = (1/12) m(w² + h²) or (1/12)m(l² + h²) or (1/12)m(l² + w²)
• Moment of Inertia of Cylinder I = (1/2)mr² or (1/12)m(3r² + h²)
• Cylindrical shell moment of inertia I = mr²
• Moment of Inertia of Cylindrical tube I = (1/2)m(r₂² + r₁²) or (1/12)m(3(r₂² + r₁²) + h²)
• Disk moment of inertia I = (1/2)mr² or (1/4)mr²
• Isosceles Triangle Moment of Inertia I = (1/2)mL²(1 - (2/3)sin²(β))
• Moment of Inertia Octahedron I - (1/10)ms²
• Point of mass moment of inertia I = mr²
• Rectangular plate moment of inertia I = (1/12)m(w² + l²)
• Moment of inertia of sphere I = (2/3)mr²
• Two-point masses moment of inertia I = (m₁m₂)r²/(m₁ + m₂)

### How to Calculate Moment of Inertia?

The steps for calculating the mass moment of inertia for various shapes are described below. To simply obtain the value, follow the following instructions and methods.

• Step 1: Make a note of the information provided in the question.
• Step 2: Get the formula and change the values in it.
• Step 3: To find the moment of inertia value, perform the necessary mathematical calculations.

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

### How to use the Moment of Inertia Calculator?

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

• Step 1: Input the unknown value's mass, distance and x in the appropriate input fields.
• Step 2: To acquire the result, click the "Calculate the Unknown" button.
• Step 3: Finally, the output field will show the moment of inertia.

Moment of Inertia Examples

Question 1: A 7 kg object is placed at 35 metres from the rotation axis. Find the inertia moment about the axis of rotation.

Solution:

Given: m = 7 kg

d = 35 m

Moment of inertia I = md²

I = 7 x 35² = 7 x 1225

= 8575

Therefore, object moment of inertia is 8575 kgm²

Question 2: An object of mass 6 kg is situated at a distance of 30 m from the axis of rotation. Calculate the moment of inertia about the axis of rotation.

Solution:

Given:

m = 6 kg

d = 30 m

Moment of inertia I = md²

I = 6 x 30² = 6 x 900

= 5400

Therefore, the object moment of inertia is 5400 kgm²

### FAQs on Moment of Inertia

1. How do you calculate the mass moment of inertia?

The moment of inertia for a point mass is just the mass times the square of the perpendicular distance to the rotation axis, I = mr^2. Since any item may be constructed from a collection of point masses, the point mass relationship provides the foundation for all other moments of inertia.

2. What does M stand for in the inertia formula?

The m stands for mass (lb m, kg) R is the distance between the rotation mass and the axis (ft, m) The sum of all other moments of inertia of an object is used to compute the moment of all other moments of inertia of an object.

3. What is the purpose of the calculating moment of inertia?

The moment of inertia of an object is a computed measure for a rigid body rotating around a fixed axis: it measures how difficult it would be to modify the rotational speed of an object.

4. What is meant by mass moment of inertia?

The mass moment of inertia, also known as rotational inertia, is a measure of a body's resistance to a change in the rotation direction of angular momentum. It describes the acceleration that an item or solid experiences when torque is applied.

5. Is there a difference between mass and inertia?

The tendency of objects to remain in their current state, whether at rest or in motion, is known as inertia. The mass of an object, or the amount of substance in it, is proportional to its inertia.