# Golf: Physics in Action

by Claire Roop, AP Physics C: Mechanics student

I will admit that I am not the most physics-savvy student, but I am much more familiar with the concepts of AP Physics C: Mechanics than I realized. I have played golf for 12 years, improved my swing to the point of the 4 handicap I have today, and taught young juniors the basics of golf. As someone who is well-versed in the golf swing, I know many of the fixes for common problems among amateur golfers. To my surprise, that ability also means I understand physics. I am just now learning to put a name with the concepts I have been using.

The golf swing applies to many of the major concepts I have learned in class: kinematics, force and Newton’s Three Laws of Motion, Conservation of Energy, Conservation of Momentum, rotational motion, and torque. While I will not incorporate all of the above in this discussion, the three most important to the success of a golf swing are the double pendulum effect, centripetal force, and torque.

## The Double Pendulum Effect

Original photograph by the author

A pendulum, a weight hung from a fixed point that freely swings under the influence of gravity, can be found in two parts of the golf swing, hence the name double pendulum effect. A golfer’s arms pivoting around the fixed point of his shoulders represent the first pendulum. The wrists are the pivot point for the golf club, the second pendulum. The two pendulums can best be seen as the golfer returns the club back to the ball in the forward swing. As the golfer begins the forward swing, the arms first pivot around the shoulders, then the club simultaneously pivots around the wrists as the golfer’s arms and club line up vertically to hit the golf ball.

## Centripetal Force

For all objects in circular motion, the net force (the centripetal force) is in the same direction as the acceleration which is toward the center of the circle. The motion of a golf swing can be thought of as a large circle with the lower body anchored as the wrists pull inward and the golf club swings outward. The further the end of the golf club is from the center of rotation (the golfer), the more speed is created. This effect can be seen in the relationship between angular and translational velocity: v = r ω where v is translational velocity, r is the radius of the circle, and ω is the angular velocity. Translational velocity and the radius share a direct relationship which means an increase in the radius will result in an increase in translational velocity. Put in a golf context, the translational velocity of the golf club head and the slower angular velocity of the golfer’s wrists create tension in the golf club. The force of tension minus a weight component of the golf club represents the centripetal force of the golf swing. An increase in distance from the center of rotation also results in an increase in centripetal force (FC = mω2r).

Original photograph by the author

## Torque

Original photograph by the author

Torque, which measures how much a force causes an object to rotate, may be the most integral part of the golf swing. There are two main areas of torque in a golf swing: wrist torque and shoulder torque. Represented as force times radius, a force applied by the hands on the golf club creates torque as the club is released down to the golf ball. More specifically, for a right-handed golfer in the forward swing, the right hand pushes (force) on the grip of the golf club as the left hand works against that motion (pivot); the distance between the right and left hands is the radius. As the right hand applies force on the club in attempt to release the club head, positive torque is created.  Similarly, the force of the wrists in the forward swing in opposition to the pivot point of the shoulders creates shoulder torque.

While several other physics concepts govern the motions of the golf swing, the double pendulum effect, centripetal force, and torque are essential to mastering the swing. Though I have used these ideas throughout my golfing history, it is helpful to back it with scientific explanations rather than trial-and-error. Any change in the mechanics of a golf swing could be the difference between hitting the ball on the putting green versus hitting it in the water. It is a common saying among golfers that golf is a mental game…well, I think it is also a game of physics.

## Works Cited

Gwynne, P. (2015, December 09). In Search Of The Perfect Golf Swing. Retrieved May 11, 2016, from https://www.insidescience.org/content/search-perfect-golf-swing/3471

Mgrdichian, L. (2006, December 18). Physics Reveals the Key to a Great Golf Swing. Retrieved May 11, 2016, from http://phys.org/news/2006-12-physics-reveals-key-great-golf.html

USGA (Producer). (2014, May). Science of Golf [Video file]. Retrieved May 12, 2016, from http://www.nbclearn.com/science-of-golf/cuecard/64728

White, R. (2008, December). Golf Swing Physics. Retrieved May 11, 2016, from http://www.tutelman.com/golf/swing/golfSwingPhysics3a.php#wristtorque

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