What is the Mass Moment of Inertia? Explanation, Uses and Calculator

The strength of materials and mechanical elements are very important subjects of design and mechanical engineering. If you take a look a closer glance at these topics, all the laws and phenomena related to these topics are dependent on the same physical laws. To understand and get a master’s in these topics, one must learn about these basic natural phenomena. 

Check: The Most Used Strength of Materials Textbooks

One of these natural and physical phenomena is the mass moment of inertia of different shapes. In this article, we would like to elaborate on the mass moment of inertia topic and its uses in mechanical fields.

Mass Moment of Inertia Calculation  

In hand calculations, the mass moment of inertia is calculated for only certain shapes. For all the shapes, the mass moment of inertia is calculated by multiplying the square of the distance of the gravitational center to the rotational axis with the mass. You can use the mass moment of inertia calculator to calculate for certain shapes that are used in hand calculations in general.


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Rectangular Prism























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Hollow Cylinder





















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The use of the mass moment of the inertia calculator is very simple. You just need to select a certain shape to be calculated and enter the required dimensional and mass values inside the brackets. Then click on the ‘Calculate!’ button to make the calculation. If you want to make another calculation, click on the ‘Reset’ button then re-enter the values. 

What is the Mass Moment of Inertia? 

Mass moment of inertia is a physical phenomenon that the resistance of a mass to rotate around an axis. So, with the increasing amount of the mass moment of inertia, the resistance to rotation increases. Various parameters affect the mass moment of inertia and resistance to rotation. 

How the Mass Moment of Inertia is Calculated?

Calculation of the mass moment of inertia is very simple. The mass of the object is multiplied by the square of the distance of to rotation axis. All kinds of shapes can be calculated with this formulation. So the important parameters related to Mass Moment of Inertia can be summarized like this;

  • Mass: Not surprisingly, mass is one of the most important parameters in the calculation of the mass moment of inertia. The increasing mass means an increasing amount of mass moment of inertia. Thus, the increasing amount of mass increases the total resistance to rotation. 
  • Shape: The shape of the object affects its gravitational center of it. If the center of gravity is affected, the distance between the center of mass and the rotation axis can be affected. So, with the increasing distance, the mass moment of inertia of the object changes. Shape changes are very important in the design and calibration of mass moment of inertia in rotating machinery. 
  • Rotation Axis: In different kinds of applications, the rotational axis is a very important parameter. Think about the calibration of a rotation of the crankshaft. In general, rotational axes are predefined in the design phase. The place of the rotation axis affects the mass moment of inertia, thus resistance to the rotation. 

 In the design phase, these parameters are considered by mechanical designers.

Mass Moment of Inertia of Certain Shapes

In hand calculations, the mass moment of inertia is generally used for certain shapes. But in professional calculations, engineers are generally used to calculate the center of gravity of the complex shapes by using special CAD tools. Then according to the data that is obtained, they can directly calculate the mass moment of inertia. 

As we stated in the calculator above, rods, disks, rectangular prisms, cylinders, hollow cylinders, and spheres are generally calculated in hand calculations.

In Which Applications and Systems, the Mass Moment of Inertia is Used?

As you understand, in rotational applications, mass moment of inertia is commonly used. Mechanical design of rotational machines is not an easy thing and lots of calculations must be made to overcome them. And the mass moment of inertia calculations are the main part of these calculations and constantly you must use the mass moment of inertia calculation. So, you can use the mass moment of the inertia calculator below. 

In these areas, mass moment of inertia calculations are made; 

  • Turbomachinery: Turbomachinery may be the biggest area where rotating components are mainly used. For example in the design of the blade structure of a gas turbine power generator. In these kinds of machines, the acceleration and the rotation speeds are very important parameters. So, the mass moment of inertia is commonly calculated to calibrate the acceleration and speed. Mass moment of inertia of the turbine blades is also affecting the total energy consumption and production. If the mass moment of inertia is very high according to the optimized value, energy consumption will increase and the energy output of the turbine will decrease. 
  • Automobile Crankshafts: In the design of the automobile crankshafts, there is a strict calculation of mass moment of inertia. The crankshaft is rotated by the reciprocating pistons and these pistons are attached to little shafts that are placed eccentrically. That eccentricity creates an unbalanced situation according to the rotation axis of the crankshaft and this unbalanced situation must be eliminated with counterweights. To make the total mass moment of inertia that originated from this imbalance, the mass moment of inertia of the counterweights must be designed expertly. 
  • Flywheels of Engines: Actually, flywheels are found in lots of rotating machinery but in engines, it eliminates the speed variations in each stroke of the pistons. The mass moment of inertia which is the resistance to rotation balances the rapid changes of pistons in each cycle. Flywheels provide a very smooth rotation of the crankshaft. So, mass moment of inertia must be calculated strictly for them. 

So, mass moment of inertia calculations is a very important part of mechanical design engineering. 

Conclusion

By preparing this article, we would not like to bother the reader with so many mathematical details about the mass moment of inertia. We created a calculator to make the mathematical side. With the mass moment of inertia calculator, we would like to give the general logic of mass moment of inertia other than ‘only a mathematical value that needs to be calculated’. 

Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

You can find out much more calculators like this in Mechanicalland! Take a look at the other engineering calculators available in Mechanicalland!

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