What Is Angular Momentum and When Is It Conserved?

Angular momentum is the rotational equivalent of linear momentum. It is conserved when the resultant external torque acting on an athlete or object is zero, or is negligible during the period being considered.

The Reasoning and Mechanism

For an athlete rotating about an axis, angular momentum is calculated using:

$$L = I\omega$$

Here, $L$ is angular momentum, $I$ is the moment of inertia, and $\omega$ is angular velocity. The SI unit of angular momentum is $\text{kg m}^2\text{s}^{-1}$.

Moment of inertia depends on the athlete's mass and how far that mass is distributed from the axis of rotation. When no resultant external torque acts, total angular momentum remains constant:

$$I_1\omega_1 = I_2\omega_2$$

For example, suppose a diver has $I_1 = 6\text{ kg m}^2$ and $\omega_1 = 2\text{ rad s}^{-1}$. The diver's angular momentum is . If tucking reduces the moment of inertia to , then .

This reflects Newton's laws in rotational motion: torque causes a change in angular momentum. Internal movements can redistribute mass and alter angular velocity, but they cannot change the system's total angular momentum without external torque.

A common misconception is that angular momentum is conserved whenever an athlete is rotating. It is conserved only when resultant external torque is zero or negligible; ground contact can create substantial torque.

Exam Technique

For IB SEHS subtopic B.2.1, define angular momentum, state $L = I\omega$, give the conservation condition, and apply it to a sporting movement. Clearly distinguish angular momentum from angular velocity and explain the inverse relationship between $I$ and $\omega$.