Biophysics Problem 44

In a high dive, why does the human body in a tucked position rotate so much faster than in an extended position?

Remember that the angular momentum is conserved.  Angular momentum is the produce \(I \;\omega,\) where \(I\) is the moment of inertia, and \(\omega\) is the angular frequency.
This question boils down to whether your moment of inertia \(I\) is more more or less when your body is tucked than when it is extended.
From your readings, you should realize that \(I\) gets less when your body larger when your body is tucked.  Because of Conservation of Angular Momentum, the angular frequency \(\omega\) must increase if \(I\) decreases.
Thus, your body rotates faster (i.e. it has a larger \(\omega\) when it is in a tucked position.