7

Moment of Inertia and Mutilation Studies of an Insect Wing

103

Table 7.1 Moment of Inertia of Regular Bodies about Different Axis

SI.

no

body

Position of

axis of rotation

Moment of inertia

Shape

1

Thin bar

a. Through

centre of

gravity and

perpendicular

to length

Ml²

12

b. Through one

end and

perpendicular

to its length

Ml²

3

2

Rectangular

Lamina

length: = a;

breadth = b

a. Passing

through center

of gravity and

perpendicular

to its plane

M



l²+b²

12



b. About an

axis in its own

plane and

passing

through one if

its ends

parallel to

x-axis

Iz = ^Mb2

12 ^{+ M}



b

2

2

Iz = ^Mb2

3

c. About an

axis in its own

plane and

passing

through one if

its ends

parallel to

y-axis

Iy = ^Ma2

12 ^{+ M}

 a

2

2

Iy = ^Ma2

3

3

Circular

lamina

a. About any

diameter

ID = ¹

4^MR2

b. About a

tangent in its

plane

Iτ = ID + M .R²

= ¹

4^{MR2 + MR2 = 5}

4^MR2

4

Elliptic

lamina

a. About the

major axis (2a)

Iz = ¹

4^Mb2

b. About the

minor axis (2b)

Iy = ¹

4^Ma2

c. About axis

tangent at the

edge in its own

plane parallel

to major axis

Iτx = ¹

4^{Mb2 + Mb = 5}

4^Mb

(continued)