Example 7.3 Find the centre of mass of a
uniform I-shaped lamina la thin flat plate)
with dimensions as shown. The mass of
the lamina is 4 kg
Answers
QUESTION:
Find the center of mass of a uniform L shaped lamina (a thin flat plate) with dimensions as shown. The mass of the lamina is 3 Kg.
ANSWER:
Choosing the X and Y axes. we have the coordinates of the vertices of the L. shaped lamina as given in the figure. We can think of the L-shape to constant of 3 square each of length 1m. The mass of each square is 1 Kg. Since the lamina is uniform.
The center of mass of each square in X,Y coordinate C
1
(1/2,1/2),C
2
(3/2,1/2). andC
3
(1/2,3/2) of the square are by,
Formula for center of mass.
X=
m
a
+m
b
+m
c
m
a
x
a
+m
b
x
b
+m
c
x
c
Y=
m
a
+m
b
+m
c
m
a
y
a
+m
b
y
b
+m
c
y
c
X=
(1+1+1)
[1(1/2)+1(3/2)+1(1/2) ]
=
6
5
m
X=
(1+1+1)
[1(1/2)+1(1/2)+1(3/2) ]
=
6
5
m
Hence, center of mass of L shape is (
6
5
,
6
5
)
