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Physics equations/Equations/Moments of inertia (small table)
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Equations
Description
[
1
]
Figure
Moment(s) of inertia
Rod
of length
L
and mass
m
(Axis of rotation at the end of the rod)
I
e
n
d
=
m
L
2
3
{\displaystyle I_{\mathrm {end} }={\frac {mL^{2}}{3}}\,\!}
Solid cylinder of radius
r
, height
h
and mass
m
I
z
=
m
r
2
2
{\displaystyle I_{z}={\frac {mr^{2}}{2}}\,\!}
I
x
=
I
y
=
1
12
m
(
3
r
2
+
h
2
)
{\displaystyle I_{x}=I_{y}={\frac {1}{12}}m\left(3r^{2}+h^{2}\right)}
Sphere
(hollow) of radius
r
and mass
m
I
=
2
m
r
2
3
{\displaystyle I={\frac {2mr^{2}}{3}}\,\!}
Ball
(solid) of radius
r
and mass
m
I
=
2
m
r
2
5
{\displaystyle I={\frac {2mr^{2}}{5}}\,\!}
↑
https://en.wikipedia.org/w/index.php?title=List_of_moments_of_inertia&oldid=582953751