Centroid / Centre of Gravity
1
3)Graity axis of body
The gravity azis of a body is the ui'ne of acion ot the gravito
ravitatin
- nat force. that acts bn the.
body
A rigid body is a collection of
s
particles The weight of each arbi
eachartice
the torce exerted on tt by
Carth. So for
gravitational attracthion of the the
riqid bocy the weights of all particles fornm a
a
parallelforce system. The resultant of all these parallel torces i
the we'ght
of the body and the resultant axis is Cau ed ravit
axis of a
body.
A bocly has a
gravity axis for each orientation relative to the
earth
b) Centre of gravity
The centte of gravity ot a
body is the point of intersectton of
al the gravity axes of the body
OR
Centre of gravity of a body is a
resultant of the distributed
point through which the
gravity forces act irrespective of the
orientation of the bodyy
Centre of mass
I+ ic the point where the entire
mass of
to be Com centrated.
a
body may
may be
be Supposex
SupP
, The Centre of mass and centre of gravity Codnude as long as
the unitorm and barallel
gravity fteld is tre ated as
) Centroid geometr cal Centre of a body.
It is dekined as
the.
general when dens ity of eterdal is uniform th rough
body the postions of centroid and centre of moss are identical:
If density varies these two points wil not Coinu'de
2 Determination of centre of 9ravtty , centre of massS and Centroid
)Determination ot centre of gravity
To determine mathematically the location of C:: of any body,
we apply prånciple of moments to the Parallel system of 9ravitatio-
-nal forces.
By Vargnon's theorem,
The moment of resultant gravitational force (u) about any qu's is
equal to Sum of moments of gravitational orces dw acting on all
Particles about the Same ax's.
w Jx dw
(lonent about y axis.)
dw
w
moment about other two axtsS
Similardy
T JJ-d z wdo
, t i fi.iiUi
1
3)Graity axis of body
The gravity azis of a body is the ui'ne of acion ot the gravito
ravitatin
- nat force. that acts bn the.
body
A rigid body is a collection of
s
particles The weight of each arbi
eachartice
the torce exerted on tt by
Carth. So for
gravitational attracthion of the the
riqid bocy the weights of all particles fornm a
a
parallelforce system. The resultant of all these parallel torces i
the we'ght
of the body and the resultant axis is Cau ed ravit
axis of a
body.
A bocly has a
gravity axis for each orientation relative to the
earth
b) Centre of gravity
The centte of gravity ot a
body is the point of intersectton of
al the gravity axes of the body
OR
Centre of gravity of a body is a
resultant of the distributed
point through which the
gravity forces act irrespective of the
orientation of the bodyy
Centre of mass
I+ ic the point where the entire
mass of
to be Com centrated.
a
body may
may be
be Supposex
SupP
, The Centre of mass and centre of gravity Codnude as long as
the unitorm and barallel
gravity fteld is tre ated as
) Centroid geometr cal Centre of a body.
It is dekined as
the.
general when dens ity of eterdal is uniform th rough
body the postions of centroid and centre of moss are identical:
If density varies these two points wil not Coinu'de
2 Determination of centre of 9ravtty , centre of massS and Centroid
)Determination ot centre of gravity
To determine mathematically the location of C:: of any body,
we apply prånciple of moments to the Parallel system of 9ravitatio-
-nal forces.
By Vargnon's theorem,
The moment of resultant gravitational force (u) about any qu's is
equal to Sum of moments of gravitational orces dw acting on all
Particles about the Same ax's.
w Jx dw
(lonent about y axis.)
dw
w
moment about other two axtsS
Similardy
T JJ-d z wdo
, t i fi.iiUi
