How Does Changing the Wheel's Axis Affect Platform Rotation?

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Homework Statement

A person stands on a platform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform is I_P. The person holds a spinning bicycle wheel with its axis horizontal. The wheel has a moment of inertia I_w and angular velocity W_W. What will be the angular velocity W_P of the platform if the person moves the axis of the wheel so that it points vertically upward?

Homework Equations

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L_initial = L_final

The Attempt at a Solution

I didn't understand why the angular momentum is conserved only in vertical axis. There is no external force, so what has happened to angular momentum in the horizontal? Wıth regard to what should I choose an axis so that I can apply the conservation?

 

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There is no external force, so what has happened to angular momentum in the horizontal?

External forces do come into play to prevent the platform from rotating horizontally. The platform is constrained to freely rotate only about a vertical axis.