# How can angular momentum not be parallel with angular velocity?

I have a quiz with the following question:

How can the angular momentum vector not be parallel to the angular velocity vector? That would mean they don't have the same direction, right?

We have this relation between angular momentum and angular speed:

Since they only differ by a scalar, how can they not have the same direction?

The comment by QuantumBrick really tells you all you need to know: "$I$ is not a scalar, but a tensor". However, sometimes it's hard to get an intuition for this. Let me try the following: