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:
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Igeneral=kmr2I_{general}= kmr^2Igeneral​=kmr2
Here are the variables for the equation
﻿﻿I
 = the moment of inertia (﻿m2kg​
)
﻿﻿k
 = the inertial constant, 0.8
﻿﻿l
 = the length of the rigid body (m)
﻿﻿m
 = the body's mass (kg)
﻿﻿r
 = distance between the centroid of the body and the axis, i.e. the radius (m)
CalculationInputs﻿﻿Inertial 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​
﻿
Output﻿﻿Generial Mass Moment of Inertia, I
:8,000.00kg m^2​
﻿
ExplanationThe 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:
Mass moment of inertia
Angular mass
Second moment of mass
Rotational mass
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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:
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Solid Cylinder - Central Axis
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Solid Cylinder - Diameter
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Cuboid
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Hoop - Central Axis
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Hoop - Diameter
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Right Solid Circular Cone 
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Right Hollow Circular Cone 
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Solid Sphere
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Hollow Sphere
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Rod - Centre Normal Axis
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Rod - End face Axis
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Regular Tetrahedron
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Regular Octahedron
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Torus
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