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Torus
This page provides a diagram and functioning calculator to compute the mass moment of inertia for a torus.
I
c
e
n
t
r
e
=
1
4
m
(
4
b
2
+
3
a
2
)
I_{centre} =\frac{1}{4}m(4b^2+3a^2)
I
ce
n
t
re
=
4
1
m
(
4
b
2
+
3
a
2
)
I
d
i
a
m
e
t
e
r
=
1
8
m
(
5
a
2
+
4
b
2
)
I_{diameter} =\frac{1}{8}m(5a^2+4b^2)
I
d
iam
e
t
er
=
8
1
m
(
5
a
2
+
4
b
2
)
The following are the variables for the equations...
I = the moment of inertia (
k
g
/
m
2
).
h = the height of the cone (m).
m = the body's mass (kg).
a = minor radius
b = major radius
Figure 1: Diagram Of The Moment of Inertia For A Torus
Moment of Inertia For A Torus Calculator
Inputs
Mass, m
:
10.00
kg
Major Radius, b
:
1.00
m
Minor Radius, a
:
0.50
m
Output
Moment of Inertia, I (centre)
:
11.88
kg m^2
I
c
e
n
t
r
e
=
1
4
m
(
4
b
2
+
3
a
2
)
I_{centre} =\frac{1}{4}m(4b^2+3a^2)
I
ce
n
t
re
=
4
1
m
(
4
b
2
+
3
a
2
)
Moment of Inertia, I (diameter)
:
6.56
kg m^2
I
d
i
a
m
e
t
e
r
=
1
8
m
(
5
a
2
+
4
b
2
)
I_{diameter} =\frac{1}{8}m(5a^2+4b^2)
I
d
iam
e
t
er
=
8
1
m
(
5
a
2
+
4
b
2
)
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