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The way in which you can start your golf swing is always an extremely interesting question and opinion amongst golfers can vary.
The best and most consistent way to start your back swing is with your left arm as this will get the club going away from the ball in a straight line and also will encourage the shoulders to rotate from the start of the golf swing. A straighter takeaway will encourage a better arc, and more importantly, a better swing path into the ball. If the club deviates from that initial 1-12 inches straight back from the ball, it is already on the inside or outside of the desired swing path, therefore enforcing more chances of missing the target left or right.
Keeping the left arm straight throughout the back swing encourages more tension and shoulder rotation during the back swing which helps create much more power in the swing. Once the left arm bends at the top, all tension and built up energy is lost and the player spends the whole of the down swing trying to rescue the swing path of the club.
This is a key area of the swing to practice when on the practice range. Use visual aids, for instance put a tee peg on the ground about 6-12 inches behind the ball and during the takeaway make sure that the club goes straight back over it, and feel which aspect of your swing is initiating this movement. This drill will help you keep the left arm straight, take it away on plane and also maintain width during the back swing.
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Starting the back swing with your hips will encourage an extremely flat takeaway, potentially leading to an over rotation of your hips and a very rounded golf swing. This type of swing will only help cause an inconsistent down swing because many players then throw their arms forwards from the top causing an out to in swing path which can potentially cause a pull, pull hook or slice shot unless managed extremely well.
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Starting the back swing with the hands will cause the club face to rotate. If it rotates too much it could potentially leave the club face pointing right or left at impact which will hugely impair the direction of the golf shot.
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It is important to start the back swing with the correct body movement as it can help determine the path of the swing. During the back swing, the right arm bends approximately 90 degrees. If this was the lead arm on the back swing then it could potentially cause the left arm to break also which would result in a loss of power.