Question

Find the centre 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 1

Explanation:

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