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Having external rotation strength to turn the bar over in the snatch or having quick elbows in the turnover of the clean is great, but you can't have a quick turnover in either lift without accelerating down adequately first. The turnover itself is not and will never be a strong movement. Think of your shoulder pre-hab/re-hab external rotation exercises: how much resistance can you use? Very little, especially relative to the weights you're snatching and cleaning.

What allows the turnover to happen at all, let alone be quick, is momentum. The movement is a follow-through, and it can't occur if you're not moving down under the bar quickly enough already. In order for that to happen, you need to actively PULL down: this is the third pull. After you've completed your final explosive hip and knee extension, move the feet and pull the elbows as high as possible and out to the sides. This action is what changes your direction at the top of the pull and gets you moving down under the bar with enough speed that you can turn the bar over into the receivng position powerfully. Try some tall snatches and tall cleans to feel what it means to really pull down rather than just falling under the bar.