Find the centre of mass of a l-shaped uniform lamina
Answers
Explanation:
Choosing the X and Y axes as shown in Fig. 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 consist of
3
squares each of length
1
m. The mass of each square is
1
kg, since the lamina is uniform. The centres of mass
C
1
,
C
2
and
C
3
of the squares are, by symmetry, their geometric centres and have coordinates
(
1
/
2
,
1
/
2
)
,
(
3
/
2.
1
/
2
)
,
(
1
/
2
,
3
/
2
)
respectively. We take the masses of the squares to be concentrated at these points. The centre of mass of the whole L shape
(
X
,
Y
)
is the centre of mass of these mass points.
Hence
X
=
[
1
(
1
/
2
)
+
1
(
3
/
2
)
+
1
(
1
/
2
)
]
k
g
m
(
1
+
1
+
1
)
k
g
=
5
6
m
Y
=
[
1
(
1
/
2
)
+
1
(
1
/
2
)
+
1
(
3
/
2
)
]
k
g
m
(
1
+
1
+
1
)
k
g
=
5
6
m
The centre of mass of the L-shape lies on the line OD. We could have guessed this without calculations. Can you tell why? Suppose, the three squares that make up the L-shaped lamina of Fig. had different masses. How will you then determine the centre of mass of the lamina?