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Mass Moment of Inertia

This page provides insight and functions to determine the mass moment of inertia for a rigid body. Sub-pages with diagrams and calculators to calculate the mass moment of inertia for various shapes can also be found here!
The general equation for the mass moment of inertia is as follows:

Igeneral=kmr2I_{general}= kmr^2

Here are the variables for the equation

  1. 
    
    = the moment of inertia (
    
    )
  2. 
    
    = the inertial constant, 0.8
  3. 
    
    = the length of the rigid body (m)
  1. 
    
    = the body's mass (kg)
  1. 
    
    = distance between the centroid of the body and the axis, i.e. the radius (m)

Calculation

Inputs



Inertial Constant, k
:0.80​



Mass of the rigid body, m
:100.00kg​



Length of the rigid body, l
:5m​



Radius of the rigid body, r
:10m​


Output



Generial Mass Moment of Inertia, I
:8,000.00kg m^2​


Explanation

The moment of inertia quantifies a body's resistance to angular acceleration about a predetermined, fixed rotational axis. It is a pivotal factor in calculating the requisite torque to achieve a specified angular acceleration.
Moment of Inertia goes by many names:
  1. Mass moment of inertia
  2. Angular mass
  3. Second moment of mass
  4. Rotational mass

Figure 1: Diagram of The Mass Moment of Inertia
Analogous to the role of mass in dictating the necessary force for a given linear acceleration, the moment of inertia serves as a key parameter in determining the effort required to induce rotational motion around a specified axis. The selection of the rotational axis significantly influences the resultant moment of inertia value, underscoring the axis's integral role in these calculations.

The Mass Moment of Inertia For Other Shapes:

To calculate the mass moment of inertia for other shapes, check out these calculators:

Solid Cylinder - Central Axis

Solid Cylinder - Diameter

Cuboid

Hoop - Central Axis

Hoop - Diameter

Right Solid Circular Cone

Right Hollow Circular Cone

Solid Sphere

Hollow Sphere

Rod - Centre Normal Axis

Rod - End face Axis

Regular Tetrahedron

Regular Octahedron

Torus

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