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



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

Mgrdichian, L. (2006, December 18). Physics Reveals the Key to a Great Golf Swing. Retrieved May 11, 2016, from

USGA (Producer). (2014, May). Science of Golf [Video file]. Retrieved May 12, 2016, from

White, R. (2008, December). Golf Swing Physics. Retrieved May 11, 2016, from

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Beautiful Music and the Laws of Physics

by Rebecca Guerreso, AP Physics 1 Student

Ludwig van Beethoven once proclaimed, “Music is … A higher revelation than all Wisdom & Philosophy.” Music plays an important role in many people’s lives, yet few know that the basis of music and its sound derive from the laws of physics. Upon hearing a stirring piano solo, one may wonder what is occurring inside the piano that results in such a beautiful sound; the mysteries of sound within a piano originate from basic physics principles. Physics phenomenon regarding waves and oscillations result in the piano creating music.

Understanding the cause of the diverse sounds a piano produces, requires knowledge of the different parts inside the instrument. When a key is pressed on the piano, a sound is heard; when the key is pressed with a larger amount of force, the sound becomes louder. This sound and its amplitude are caused by four major components of the piano: the hammer, the damper, strings, and the soundboard. Every key has a damper, hammer, and either one, two, or three strings. Each of these parts has a different function; the damper stops the string from vibrating to ensure that when a key is pressed, only that key makes a sound. The hammer strikes the string, resulting in vibrations. The soundboard amplifies the string’s vibrations to make the sound louder. When a key is pressed, the damper is released so that the string can make a sound, the hammer strikes the string, and the string vibrates to make a sound.

A typical piano contains eighty-eight keys and has a range of seven different octaves. Starting from the right side of the piano, the first key has the highest pitch, and the pitch of each key after it decreases. The properties of the string for each key determine the pitch that the key will produce. Physics principles have determined that a longer string results in a lower pitch because the fundamental frequency is equal to the quotient of the velocity and two times the length, f = v/(2L). Inside the piano, the strings increase in length for keys with lower pitches, but if only the length were changed for each string, then the strings would exceed the height of the piano. Therefore, to lower a pitch of a key, the length is increased along with the diameter of the string. This concept holds true for all keys to the right of middle C; the keys to the left of middle C must be adjusted differently. If the diameter and length continued to increase, the string would not be able to vibrate regularly after a certain point, which would result in the production of an irregular sound. The keys to the left of middle C have a very low pitch; to accommodate this low pitch, the normal steel wires are wound with a copper wire. By winding the strings together, the total mass of the string increases, allowing the string to vibrate properly because if the mass is increased then the frequency of the string decreases. These physics principles result in octaves on musical instruments; physics has proven that doubling the length of the string decreases the resulting sound by an octave.

Typically, the frequency of each string on a piano ranges from sixteen hertz to seven thousand and nine hundred hertz, while wavelength varies from four centimeters to two thousand and one hundred centimeters. The ranges in frequencies and wavelengths cause each key to produce a different sound. A piano contains seven octaves and these seven octaves repeat throughout the eighty-eight keys on the piano (first key on far left is A; last key on far right is C). Each note on the piano has a fundamental frequency; to increase the note by one octave, the fundamental frequency must be doubled; to increase the note by two octaves, the fundamental frequency must be quadrupled (or the first level frequency must be doubled). The changed frequency creates different tones for each note.

Another factor that affects the piano’s sound are the three pedals. On a standard upright piano, the pedal farthest to the right is called the damper pedal, and is the most commonly used pedal. This pedal allows the notes to be played much more smoothly. When the damper pedal is pressed, the dampers are released from the strings. Consequently, when a note is played all the strings vibrate since there are no dampers to inhibit vibrations. The celeste pedal is the middle pedal; it drops a felt pad onto the tops of the strings in order to lower the amount of vibrations on the string, and in effect, make the sound much quieter. The pedal to the far left is the una corda pedal; it shifts the hammers so that it strikes fewer strings than usual, creating a softer sound because there are less vibrations.

The piano and the sounds it produces utilize many physics principles. The strings within the piano operate at different frequencies, which result in different wavelengths; this is why the piano has the ability to produce such a vast range of notes. Pianos go “out of tune,” meaning the keys produce incorrect sounds, throughout the year because the temperature fluctuates, which slightly changes the speed of sound in air. The sounds the piano creates is a language that everybody in the world can understand—sounds created by manipulating laws of physics. Henry Wadsworth Longfellow once marveled, “Music is the universal language of mankind,”and I could add physics makes music possible.

Works Cited

Joyner, Lauren, Erika Littman, Emily Massey, and Johanna Robertson. “Piano Physics.” String Vibration. N.p., 2009. Web. 09 May 2016.

Rack, C. Mckinney And Nsf. “Physics of the Piano.” Physics of the Piano N Giordano — Purdue University (n.d.): n. pag. Web. 9 May 2016.

Suits, B. H. “Frequencies of Musical Notes, A4 = 440 Hz.” Frequencies of Musical Notes, A4 = 440 Hz. Michigan Technolgical University, 1998. Web. 09 May 2016.

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The Physics of Skydiving

by Ashley Hazel AP Physics 1 Student

Every one has heard of the extreme sport of skydiving, yet does everyone know the physics involved with it? Physics plays a monumental role in every aspect of our lives, and for this intense hobby, physics dishes up a major dose. So let’s break things down.

The first jump.

Once you leave that plane, your heart is racing, your palms are sweating, and probably the only thing on your mind is “Ahh!.” But, have you ever stopped to think about what’s going on around you as you joyfully plummet towards the ground? As you are capturing those Instagram-worthy Go-Pro selfies, there are two forces acting on you: gravitational pull and friction with the air. As you leave the plane, Earth’s gravitational pull will carry you straight towards the ground, and you’ll gain speed with each second. While you begin to travel, the resistance from the air around you begins to increase and pushes up in the opposite direction of your fall (luckily it’s not as strong as gravity). Thanks to the relationship between gravity and air resistance, you won’t keep falling at a rapidly increasing speed, but as your speed increases, so does air resistance. The air resistance will keep increasing until it reaches the magnitude of the force of gravity. Once this happens, the forces become balanced, and you’ll no longer accelerate.

Body Position

Ever heard of the term aerodynamics? Well, it plays a major role in skydiving, as well. The position and shape of your body dictate your speed as you fall. For example, say you and your friend decided to race down. You go with the method of tucking your arms and legs in as tight as you can into your body. Your friend, on the other hand, decides to go full flying squirrel. You’ll notice that as you fall, like the graceful armadillo you embodied, your friend will lag behind you because of the difference in body positions. Your stretched-out friend has more surface area than you do. Air resistance has a greater surface to work on, thus slowing the body down. However, while you might be the speedy one of the group, stretching out while falling is actually a better skydiving technique because this position creates dynamic stability – keeping you more stable as you descend.

The Parachute

Now comes the moment of truth: the parachute. This simple little device holds the most important job of all-SLOWING YOU DOWN. But how? The answer is simple, air resistance. Just as your body position controlled your speed, the parachute’s broad surface area works to keep you from regretting your spontaneous skydiving adventure. The parachute’s huge size proves vital and is the sole reason you can significantly slow down to a speed that promises safety. This significant change in speed is why you always see the huge snap up once the parachute has been released. The huge amount of air being trapped by the parachute causes a dramatic slowdown.

Skydiving is no joke and neither is the physics involved with it. These forces that so many of us remain unaware of are responsible for so many great things in the world. Physics allows us to jump out of planes safely. I mean what else can do that, right?!? So maybe if you ever work up the nerve to go skydiving you can stop and think about what’s really going on around you. Maybe even share it with your diving instructor. Your extensive and intriguing knowledge might even make up for that full face of hair you gave him during the jump.


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Everyday Physics: Dancing

by Sarah McPherson, AP Physics 1

When looking at a dancer, the eye sees impressive movement. Behind every performance are hours of practice, sweat, and dedication. After it’s all broken down, one can find the clockwork in dancing – physics.

A major factor in dancing is balance. Dancers have to focus on their centers of gravity when performing, for if they lean too far forward, their center of mass could go beyond the base of support, and they could fall. Balancing is even more difficult if there are partners dancing together; however, dancers can use physics to their advantage. If their centers of gravity are used correctly, the end result can be a stunning visual. For their centers of gravity to be supported, physical connection, or tension, is needed. The partners pulling on each other can help each other balance. The diagram below is a great illustration of the forces working on them.

The force of gravity is pulling them down and keeping them on the floor; likewise, the weight vectors from their centers of gravity point directly down, even though they are slightly tilted. Without the tension of their arms holding each other, both of the dancers would more than likely fall – especially the girl. Holding themselves together in this fashion creates one unit with a center of mass located somewhere between each dancer and over the base of support offered by the male dancer’s feet.

Physics also applies to swing dancing. This partner dance requires focus and momentum. For example, a very famous move in swing dancing is called “The 6 O’clock.” The female partner is directly above the male partner with her arms wrapped around his neck. The female is representative of the hour hand while her counterpart is the minute hand.

In order to reach this position, the female has to get a running start to reach the male, and then jump high enough for him to catch her. The woman’s kinetic energy during running is converted to gravitational potential energy with the assistance of the man performing work to lift the woman higher.

Though it may seem unlikely, physics is a key part of dancing. Without this science, the dancers wouldn’t be able achieve certain movements and the dance would be dull. Physics brings excitement to the dance!


About the author: Sarah McPherson is a student in AP Physics 1 and is also the Drum Major for the Marching Grizzlies. In addition, she is the artist of the featured image in the page header.

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