A Classical Approach of Newtonian Mechanics

9 ANGULAR MOMENTUM 9.4 Angular momentum of a multi-component system



d r^ r

×

where I = (1/12) M (2 b)^2 = (1/3) M b^2 is the rod’s moment of inertia (about
a perpendicular axis passing through its mid-point). Conservation of angular
momentum yields

l = lJ + L, (9.41)

or
m v d
ω =
I + m d^2

. (9.42)

Worked example 9.1: Angular momentum of a missile

Question: A missile of mass m = 2.3 104 kg flies level to the ground at an altitude

of d = 10, 000 m with constant speed v = 210 m/s. What is the magnitude of the

missile’s angular momentum relative to a point on the ground directly below its

flight path?

v

O ground

Answer: The missile’s angular momentum about point O is

L = m v r sin θ,

where θ is the angle subtended between the missile’s velocity vector and its posi-

tion vector relative to O. However,

r sin θ = d,

where d is the distance of closest approach of the missile to point O. Hence,

L = m v d = (2.3 × 104 ) × 210 × (1 × 104 ) = 4.83 × 1010 kg m^2 /s.