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Page # 8
Sol.
(i)
(ii)
(iii)
Ex.2
Sol.
ROTATIONAL DYNAMICS
Moment of inertia of particle on left is I1 = m1r12.
Moment of Inertia of particle on right is I2 = m2r22.
Moment of Inertia of the system about AB is
I = I1+ I2 = m1r12 + m2r22
Moment of inertia of particle on left is I1 = 0
Moment of Inertia of the system about CD is
I = I1 + I2 = 0 + m2 (r1 + r2)2
Moment of inertia of particle on left is I1 = 0
Moment of inertia of particle on right is I2 = 0
Moment of Inertia of the system about EF is
I = I1 + I2 = 0 + 0
Three light rods, each of length 2 , are joined together to form a triangle. Three particles
A, B, C of masses m, 2m, 3m are fixed to the vertices of the triangle. Find the moment
of inertia of the resulting body about
(a) an axis through A perpendicular to the plane ABC,
(b) an axis passing through A and the midpoint of BC.
X
A
(a) B is at a distant 2 from the axis XY so the moment of
m
inertia of B (IB) about XY is 2 m (2 )2
Y
Similarly Ic about XY is 3m (2 )2 and IA about XY is m(0)2
2l
2l
Therefore the moment of inertia of the body about XY is
2m (2 )2 + 3 m(2 )2 + m(0)2 = 20 m 2
B
(b) IA about X' Y' = m(0)2
C
2
3m
IB about X' Y' = 2m ( )
2m
IC about X' Y' = 3m ( )2
Therefore the moment of inertia of the body about X' Y' is
m(0)2 + 2m( )2 + 3m( )2 = 5 m 2
X'
A
m
B
C
3m
2m
Y'
Ex.3
Sol.
Four particles each of mass m are kept at the four corners of a square of edge a. Find
the moment of inertia of the system about a line perpendicular to the plane of the
square and passing through the centre of the square.
The perpendicular distance of every particle from
the given line is a / 2 . The moment of inertia of
m
m
1
2
2
ma
one particle is, therefore, m( a / 2 ) =
. The
2
moment of inertia of the system is,
therefore, 4
1 2
ma = 2 ma2.
2
m
m
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