Angular momentum

Two equations cover the two situations, and the AP Physics 1 equation sheet prints both.

For a rigid system rotating about a specified axis, EK 6.3.A.1 gives

For an object moving relative to a chosen point, EK 6.3.A.2 gives

where $r$ is the distance from the point to the object, $v$ its speed, and $\theta$ the angle between the radial direction and the velocity. Units are $\text{kg}\cdot\text{m}^2/\text{s}$.

An object traveling in a straight line has angular momentum. This is the result that surprises people. EK 6.3.A.2.ii says the measured value depends on the distance between the reference point and the object, its mass, its speed and that angle. A car driving past you at constant velocity has a constant nonzero $L$ about where you stand, and zero about any point on its own path.

Pick the axis before you compute. EK 6.3.A.2.i states that the selection of the axis influences the determination of the angular momentum. It is not a property of the object alone.

AP Physics C: Mechanics writes it as a vector, $\vec{L} = \vec{r}\times\vec{p} = I\vec{\omega}$. AP Physics 1 works with magnitudes and a sign for the sense of rotation.

Angular momentum changes only when an external torque acts, through angular impulse.