9 ANGULAR MOMENTUM
9 Angular momentum
9.1 Introduction
Two physical quantities are noticeable by their absence in Table 3. Namely, mo-
mentum, and its rotational concomitant angular momentum. It turns out that
angular momentum is a sufficiently important concept to merit a separate discus-
sion.
9.2 Angular momentum of a point particle
Consider a particle of mass m, position vector r, and instantaneous velocity v,
which rotates about an axis passing through the origin of our coordinate system.
We know that the particle’s linear momentum is written
p = m v, (9.1)and satisfies (^) dp
= f, (9.2)
dt
where f is the force acting on the particle. Let us search for the rotational equiv-
alent of p.
Consider the quantity
l = r × p. (9.3)
This quantity—which is known as angular momentum—is a vector of magnitude
l = r p sin θ, (9.4)
where θ is the angle subtended between the directions of r and p. The direction of
l is defined to be mutually perpendicular to the directions of r and p, in the sense
given by the right-hand grip rule. In other words, if vector r rotates onto vector
p (through an angle less than 180 ◦), and the fingers of the right-hand are aligned
with this rotation, then the thumb of the right-hand indicates the direction of l.
See Fig. 85.