Mom
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!" 0Moment of Inertia (About Centroid) '( )* " +,&- ./% & $ :49 8Center of Gravity) 1 2 '+ )* 3/ 45 67 )* $ C 3; '< = *! #> (diagonal) ! *3 7 $
'( )* Cx @ "< & "/2 & A>, & Surface Area Lateral Area + Base Area
: / 3?" +,&-Centroid coordinates Cy 125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes '( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
'( )* Cx
B* / 3?C " +,&-Centroid coordinates Cy
Cz
EF ?G * D "< & 125 : < 8H" / 3? Volume Mass Surface Area 4 I rL Moment Of Inertia about Centroidal axes '( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Thick cylinder with open ends <"? / 3?C '( )* " +,&-Centroid coordinates Cy Cz
@ "< & Surface Area
125 Volume
: < Mass
Moment Of Inertia about Centroidal axes '( )* 45 % & IXcXc IYcYc IZcZc 2 2 2 2 2 2 (m/12)(3r1 + 3r2 + h ) (m/12)(3r1 + 3r2 + h ) (m/2)(r12+r22) h: height of the cylinder / 3? J is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Properties of Half Cylinder : / 3?-K / '( )* " +,&-Centroid coordinates Cx Cy Cz @ "< & "/2 & A>, & Surface Area Lateral Area + Base Area
125 Volume
: < Mass
Moment Of Inertia about Centroidal axes '( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Half Cylindrical Shell B* / 3?-K / '( )* " +,&-Centroid coordinates Cy
EF ?G * D "< & 8H" / 3?L Surface Area
125 Volume
Cz : < Mass
2 I rL Moment Of Inertia about Centroidal axes '( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
'( )* Cx "< & Surface Area
sphere >*) " +,&-Centroid coordinates Cy 125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Spherical shell B* >*) '( )* " +,&-Centroid coordinates Cx Cy 0 "< & 125 Volume Surface Area
Cz 0 : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
"< & Surface Area
Hemisphere : >*)K / '( )* " +,&-Centroid coordinates Cy 0 125 Volume
Cz
: < Mass
3Ir2 Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx "< & Surface Area
Hemispherical Shell B* >*)K / '( )* " +,&-Centroid coordinates Cy 0 125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx "< & Surface Area
Rectangular Block M" 3: NO : '( )* " +,&-Centroid coordinates Cy 0 125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
4P" / 3?Elliptical Cylinder ! '( )* " +,&-Centroid coordinates Cx Cy 0 &
A >,
& @ "< & "/2 Surface Area = Lateral Area + Base Area
125 Volume
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cz : < Mass
IZcZc
P Slender Rod Q" R" '( )* " +,&-Centroid coordinates Cx Cy 0 L/2 "< & 125 Surface Area Volume
Cz 0 : < Mass m
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Quarter Circular Slender Rod &Q '( )* " +,&-Centroid coordinates Cy
"< & Surface Area
125 Volume
Cz 0 : < Mass m
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc 2 2 2 2 2 m r (1/2 – 4/I ) m r (1/2 – 4/I ) m r (1– 8/I2) is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Right Circular Cone S4*T '( )* " +,&-Centroid coordinates Cy 0
@ "< & "/2 & A>, & Surface Area Lateral Area + Base Area
125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Right Circular Conical Shell U* S4*T '( )* " +,&-Centroid coordinates Cy 0
"< & Surface Area 0 , *" VW E F ?G *
125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Half Circular Cone X S4*T K / '( )* " +,&-Centroid coordinates Cy
"< & Surface Area
125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Half Circular Conical Shell U* S4*T K / '( )* " +,&-Centroid coordinates Cx Cy Cz "< & Surface Area
125 Volume
: < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Trirectangular Tetrahedron + M+ *7 '( )* " +,&-Centroid coordinates Cx Cy (1/4) b (1/4) a "< & 125 Surface Area Volume
Cz (1/4) h : < Mass
(1/6) abh Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
IZcZc
Thin disk H" Y * '( )* " +,&-Centroid coordinates Cx Cy 0 "< & 125 Surface Area Volume
Cz 0 : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc 2 2 (1/4) m r (1/4) m r (1/2) m r 2 is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
'( )* Cx "< & Surface Area
" & " +,&-Centroid coordinates Cy 0 125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Thin Rectangular Plate H" '" 3: '( )* " +,&-Centroid coordinates Cx Cy b/2 0 "< & 125 Surface Area Volume
Cz h/2 : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
!" 0Moment of Inertia (About Centroid) '( )* " +,&- ./% & $ :49 8Center of Gravity) 1 2 '+ )* 3/ 45 67 )* $ C 3; '< = *! #> (diagonal) ! *3 7 $
'( )* Cx @ "< & "/2 & A>, & Surface Area Lateral Area + Base Area
: / 3?" +,&-Centroid coordinates Cy 125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes '( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
'( )* Cx
B* / 3?C " +,&-Centroid coordinates Cy
Cz
EF ?G * D "< & 125 : < 8H" / 3? Volume Mass Surface Area 4 I rL Moment Of Inertia about Centroidal axes '( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Thick cylinder with open ends <"? / 3?C '( )* " +,&-Centroid coordinates Cy Cz
@ "< & Surface Area
125 Volume
: < Mass
Moment Of Inertia about Centroidal axes '( )* 45 % & IXcXc IYcYc IZcZc 2 2 2 2 2 2 (m/12)(3r1 + 3r2 + h ) (m/12)(3r1 + 3r2 + h ) (m/2)(r12+r22) h: height of the cylinder / 3? J is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Properties of Half Cylinder : / 3?-K / '( )* " +,&-Centroid coordinates Cx Cy Cz @ "< & "/2 & A>, & Surface Area Lateral Area + Base Area
125 Volume
: < Mass
Moment Of Inertia about Centroidal axes '( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Half Cylindrical Shell B* / 3?-K / '( )* " +,&-Centroid coordinates Cy
EF ?G * D "< & 8H" / 3?L Surface Area
125 Volume
Cz : < Mass
2 I rL Moment Of Inertia about Centroidal axes '( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
'( )* Cx "< & Surface Area
sphere >*) " +,&-Centroid coordinates Cy 125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Spherical shell B* >*) '( )* " +,&-Centroid coordinates Cx Cy 0 "< & 125 Volume Surface Area
Cz 0 : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
"< & Surface Area
Hemisphere : >*)K / '( )* " +,&-Centroid coordinates Cy 0 125 Volume
Cz
: < Mass
3Ir2 Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx "< & Surface Area
Hemispherical Shell B* >*)K / '( )* " +,&-Centroid coordinates Cy 0 125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx "< & Surface Area
Rectangular Block M" 3: NO : '( )* " +,&-Centroid coordinates Cy 0 125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
4P" / 3?Elliptical Cylinder ! '( )* " +,&-Centroid coordinates Cx Cy 0 &
A >,
& @ "< & "/2 Surface Area = Lateral Area + Base Area
125 Volume
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cz : < Mass
IZcZc
P Slender Rod Q" R" '( )* " +,&-Centroid coordinates Cx Cy 0 L/2 "< & 125 Surface Area Volume
Cz 0 : < Mass m
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Quarter Circular Slender Rod &Q '( )* " +,&-Centroid coordinates Cy
"< & Surface Area
125 Volume
Cz 0 : < Mass m
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc 2 2 2 2 2 m r (1/2 – 4/I ) m r (1/2 – 4/I ) m r (1– 8/I2) is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Right Circular Cone S4*T '( )* " +,&-Centroid coordinates Cy 0
@ "< & "/2 & A>, & Surface Area Lateral Area + Base Area
125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Right Circular Conical Shell U* S4*T '( )* " +,&-Centroid coordinates Cy 0
"< & Surface Area 0 , *" VW E F ?G *
125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Cx
Half Circular Cone X S4*T K / '( )* " +,&-Centroid coordinates Cy
"< & Surface Area
125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Half Circular Conical Shell U* S4*T K / '( )* " +,&-Centroid coordinates Cx Cy Cz "< & Surface Area
125 Volume
: < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Trirectangular Tetrahedron + M+ *7 '( )* " +,&-Centroid coordinates Cx Cy (1/4) b (1/4) a "< & 125 Surface Area Volume
Cz (1/4) h : < Mass
(1/6) abh Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
IZcZc
Thin disk H" Y * '( )* " +,&-Centroid coordinates Cx Cy 0 "< & 125 Surface Area Volume
Cz 0 : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc 2 2 (1/4) m r (1/4) m r (1/2) m r 2 is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
'( )* Cx "< & Surface Area
" & " +,&-Centroid coordinates Cy 0 125 Volume
Cz : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
Thin Rectangular Plate H" '" 3: '( )* " +,&-Centroid coordinates Cx Cy b/2 0 "< & 125 Surface Area Volume
Cz h/2 : < Mass
Moment Of Inertia about Centroidal axes'( )* 45 % & IXcXc IYcYc IZcZc
is the mass of the entire body. 1 2 : ) is the density of the body. 1 2 ( )
