Moment zotrvačnosti
I
{\displaystyle I}
fyzikálna veličina , ktorá vyplýva zo vzťahu
I
=
∫
r
2
d
m
{\displaystyle I=\int r^{2}dm\,\!}
kde
r
{\displaystyle r}
d
m
{\displaystyle \mathrm {d} m}
popis
tvar telesa
moment zotrvačnosti
poznámka
dutá valcová plocha bez dna a veka, s polomerom
r
{\displaystyle r}
m
{\displaystyle m}
I
=
m
r
2
{\displaystyle I=mr^{2}\,}
—
dutý hrubostenný valec bez dna a veka vnút. polomer
r
1
{\displaystyle r_{1}}
r
2
{\displaystyle r_{2}}
m
{\displaystyle m}
I
z
=
1
2
m
(
r
1
2
+
r
2
2
)
{\displaystyle I_{z}={\frac {1}{2}}m({r_{1}}^{2}+{r_{2}}^{2})}
I
x
=
I
y
=
1
12
m
{\displaystyle I_{x}=I_{y}={\frac {1}{12}}m}
—
plný valec s polomerom
r
{\displaystyle r}
h
{\displaystyle h}
m
{\displaystyle m}
I
z
=
1
2
m
r
2
{\displaystyle I_{z}={\frac {1}{2}}mr^{2}}
I
x
=
I
y
=
1
12
m
(
3
r
2
+
h
2
)
{\displaystyle I_{x}=I_{y}={\frac {1}{12}}m(3r^{2}+h^{2})}
—
tenký disk s polomerom
r
{\displaystyle r}
m
{\displaystyle m}
I
z
=
1
2
m
r
2
{\displaystyle I_{z}={\frac {1}{2}}mr^{2}}
I
x
=
I
y
=
1
4
m
r
2
{\displaystyle I_{x}=I_{y}={\frac {1}{4}}mr^{2}}
—
plná guľa s polomerom
r
{\displaystyle r}
m
{\displaystyle m}
I
=
2
5
m
r
2
{\displaystyle I={\frac {2}{5}}mr^{2}}
—
dutá guľová plocha s polomerom
r
{\displaystyle r}
m
{\displaystyle m}
I
=
2
3
m
r
2
{\displaystyle I={\frac {2}{3}}mr^{2}}
—
kužeľ (pravouhlý) s polomerom
r
{\displaystyle r}
h
{\displaystyle h}
m
{\displaystyle m}
I
z
=
3
10
m
r
2
{\displaystyle I_{z}={\frac {3}{10}}mr^{2}\,\!}
I
x
=
I
y
=
3
5
m
(
r
2
/
4
+
h
2
)
{\displaystyle I_{x}=I_{y}={\frac {3}{5}}m(r^{2}/4+h^{2})\,\!}
—
plný kváder s výškou
h
{\displaystyle h}
w
{\displaystyle w}
d
{\displaystyle d}
m
{\displaystyle m}
I
h
=
1
12
m
(
w
2
+
d
2
)
{\displaystyle I_{h}={\frac {1}{12}}m(w^{2}+d^{2})}
I
w
=
1
12
m
(
h
2
+
d
2
)
{\displaystyle I_{w}={\frac {1}{12}}m(h^{2}+d^{2})}
I
d
=
1
12
m
(
h
2
+
w
2
)
{\displaystyle I_{d}={\frac {1}{12}}m(h^{2}+w^{2})}
pre podobne orientovanú kocku s dlžkou strany
s
{\displaystyle s}
M
{\displaystyle M}
I
C
M
=
1
6
m
s
2
{\displaystyle I_{CM}={\frac {1}{6}}ms^{2}}
tyč s dĺžkou
L
{\displaystyle L}
m
{\displaystyle m}
I
c
e
n
t
e
r
=
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