You're right! Angular momentum is measured in kg m² rad s⁻¹. It's a common misconception that it's not, and the confusion might arise from a few things:

* Radian is dimensionless: Radian is a unit of angle and is considered dimensionless in the SI system. This can lead to people thinking it's not included in the unit.

* Focus on the magnitude: Often, the angular momentum is only expressed as the magnitude, which is kg m² s⁻¹, leading to the omission of the radian.

* Alternative units: While kg m² rad s⁻¹ is the SI unit, some fields may use other units like kg m² / s.

Here's why the radian is important in angular momentum:

* Angular velocity: Angular velocity is measured in radians per second (rad/s). Angular momentum is the product of moment of inertia (kg m²) and angular velocity. So, the radian appears naturally in the unit.

* Dimensional consistency: Including the radian ensures the correct dimensional analysis of angular momentum equations and relationships.

In summary: While the radian might not always be explicitly stated, it's essential for accurate representation and understanding of the unit for angular momentum.