Mass Moment of Inertia and other Geometrical Properties

297

APPENDIX II Mass Moment of Inertia and other Geometrical Properties

(a)

Areas and Second Moments of Area

Ix

.2bh 12

3

Iy

.2- hb

3

A

bh

Ix

1

lr~

I .. I

-I

12

Rectangular Area

1'7~\\

tx

,, ..

&-

I

.. 1

Ix

.2...bh 3

A

.!..bh 2

r-~h-

36

Triangular Area

:~

X.

~ Circular Area

Ix

.!.. n:r

4

Iy

.!.. n:r

4

A

n:r 2

4

4

298

~

-rX-

41'"

t,

2. 3tr

Iy

2. 3tr

4

8

4

8

::..-- ~1T

3tr2

A

2

Semicircular Area

t,

{r

4

(S - ~

sin

2S)

Iy

{r

4

(s

sin

2S)

A

Sr 2

X

+

~

Circular Sector Area

G

I

---j-------l.....,--x

Quarter Circular Area

41"

/3.rr

Ix

..2..-

3tr4

Iy

..2..-

3t

A

3tr2

16

16

4

r4

(b)

Volumes and Mass Moments of Inertia

r ~

ta G

I yy

1 [2 _m 12

I xx

=

X

I yy =

..

~

• y

SlenderRr

I xx

299

.!. ml?

I zz

3

3

Thin Circular Disk

I yy

.!.4 mR

2

A~ I

I

4I.i

Thin Ring

.!.2 mR

2

0

300

Sphere

l:5.. mR

2

v

4 R3 _Jt

3

Hemisphere

v

0.259 mR2

X

-2J t

3

Solid Cylinder

v

R3

301

Solid Cone

v

G

Thin Rectangular Plate

.2.. ma? 12