In Progress
Lesson 1, Topic 1
In Progress

# Conservation of angular momentum

If τext = o, Eq. (28b) reduces to

dL/dt = 0

or L = constant ………………………………………………………………………………(29a)

Thus, if the total external torque on a system of particles is zero, then the total angular momentum of the system is conserved. i.e., remains constant. Eq. (29a) is equivalent to three scalar equations.

Lx =K1 , Ly =K2, Lz =K3 …………………………………………………………………….(29b)

Here K1 , K2, and K3 are constants : Lx, Ly and Lz are the components of the total angular momentum vector L along the x, y and z axes respectively. The statement that the total angular momentum is conserved means that each of these three components is conserved.

Eq. (29a) is the rotational analogue of Eq. (18a) i.e., the conservation law of the total linear momentum for a system of particles. Like Eq. (18a), it has applications in many practical situations. We shall look at a few of the interesting applications later on in this chapter.

Example 5
Find the torque of a force (7i + 3j – 5k) from the origin. The force acts on a particle whose position vector is i j + k.

Here r = i – j + k

and F = 7i + 3j – 5k

Example 6
Show that the angular momentum about any point of a single particle moving with constant velocity remain constant throughout the motion. 