Right Solid Circular Cone

This page provides a diagram and functioning calculator to compute the mass moment of inertia for a cone around it's z axis, an axis through the tip, the base and the centre of mass. 
﻿
Iz axis=13mr2I_{z\ axis} = \frac{1}{3}mr^2Iz axis​=31​mr2
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Itip=m(320r2+35h2)I_{tip} =m(\frac{3}{20}r^2+\frac{3}{5}h^2)Itip​=m(203​r2+53​h2)
The following are the variables for the equations...
I = the moment of inertia (﻿kg/m2
).
h = the height of the cone (m).
m = the body's mass (kg).
r = distance between the centroid of the body and the axis, i.e. the radius (m).
﻿
Ibase=m(320r2+110h2)I_{base} =m(\frac{3}{20}r^2+\frac{1}{10}h^2)Ibase​=m(203​r2+101​h2)
﻿
Icentre mass=m(320r2+380h2)I_{centre\ mass} =m(\frac{3}{20}r^2+\frac{3}{80}h^2)Icentre mass​=m(203​r2+803​h2)
﻿
﻿
Moment of Inertia For A Cone CalculatorInputs﻿﻿Mass, m
:15.00kg​
﻿
﻿﻿Cone height, h
:3.00m​
﻿
﻿﻿Radius, r
:2.50m​
﻿
Output﻿﻿Moment of Inertia, I (general)
:31.25kg m^2​
﻿
﻿
Igeneral=13mr2I_{general} = \frac{1}{3}mr^2Igeneral​=31​mr2
﻿﻿Moment of Inertia, I (tip)
:95.06kg m^2​
﻿
﻿
Itip=m(320r2+35h2)I_{tip} =m(\frac{3}{20}r^2+\frac{3}{5}h^2)Itip​=m(203​r2+53​h2)
﻿﻿Moment of Inertia, I (base)
:27.56kg m^2​
﻿
﻿
Ibase=m(320r2+110h2)I_{base} =m(\frac{3}{20}r^2+\frac{1}{10}h^2)Ibase​=m(203​r2+101​h2)
﻿﻿Moment of Inertia, I (centre mass)
:19.13kg m^2​
﻿
﻿
Icentre mass=m(320r2+380h2)I_{centre\ mass} =\\m(\frac{3}{20}r^2+\frac{3}{80}h^2)Icentre mass​=m(203​r2+803​h2)
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