Section 45 Moments of inertia

We begin by considering a system of n point masses m1, m2, . . . , mn situated at perpendicular distances d1, d2, . . . , dn from a straight line L . Then the quantity

ILm1d 2 1m2d

2 2 . . .mnd

is called the moment of inertia of the system of particles about L . If M/ml/ m2/. . ./mn is the total mass of the n particles, the length kL defined by

Mk2LIL,

or equivalently by

kL(IL=M) 1=2

,

is called the radius of gyration of the particles about the line L .