As you start to ski faster, you need to put more power into each turn. To do that, you need to tip the hip.
Starting at home, stand sideways, three feet away from your dining room table, weight evenly distributed on both legs. Keeping your torso stiff, place your hand on the table and bend your elbow. As you lean in, notice how your weight moves to the inside leg. That's the equivalent of weighting your uphill ski—and it's the wrong position for powerful turning.
To get it right, unlock your hip and kink your opposite oblique (your love-handle zone) as your butt sinks toward the floor. Pull your inside knee up and in. Notice how your weight shifts to the leg that's farthest from the table—or what would be your downhill ski? This is the stance used by every top racer and freeskier to harness the G-forces of high-speed turns.
Now, try it at moderate speed on a groomed run (Figs. 1 through 3). The closer you can drop your butt to the snow, the more dynamic and powerful you'll become. When you can use your hip to arc high-speed turns on the groomed, you're ready to arc 'em on big mountains.