Greg Kennedy Twice Greg has entered the highest- Gravity (of course!) innovative juggler level juggling competition, the Definition International Jugglers Association Gravity is the force of attraction Championships. On both occasions he between all masses in the universe; Study Guide received their highest honor, the Gold especially the attraction of the earth's Medal. In 1996, his original presenta- mass for bodies near its surface. It is Kinetics: The Physics of tion of "Hemisphere" won him first gravity that causes all objects to be place in the Individuals competition, pulled downward toward the ground Juggling taking Gold. In 2002, he returned, (or more specifically towards the Can anything be fun about the study combining efforts with partner Chris center of the earth). of physics? Will we ever use these Ivey, and as the duo "Saccade" won things in our real lives? Gold again in the Teams competition. Equation Two bodies of matter attract each If you are juggler Greg Kennedy, the Greg continues to receive praise and other proportionally to their masses answer to both of these questions is recognition from his peers for his and inversely proportional to the emphatically yes. Greg, whose mind original contributions, broadening the square of distance between them. If for logic and science led him first to a fields of juggling and performance art. the mass of one body is designated career in engineering, has discovered He presently balances his performing as M, the mass of the other as m, the the pleasure and challenge of career with a pursuit of juggling distance between them is r, and G is creating performance art using the innovation, experimenting with new the universal gravitational constant, fundamental concepts of physics. His shapes and surfaces as well as then the force of attraction between juggling shows, which are as mind- practicing traditional skills. the two bodies is: boggling as they are entertaining, illustrate the principles of motion, Physics and Juggling F = G Mm light, energy and of course, gravity. r2 While watching juggling, it’s easy to be But they also illustrate something mesmerized by the movement and else: that determination and forget that the demonstration can be What the universal gravity equation imagination can turn an academic says is that as two objects are viewed as a lesson in physics. From pursuit into a powerful art form. attracted and get closer together, the the simplest throw and catch of one ball, a multitude of concepts of force increases and the acceleration Sit back and enjoy Greg’s show, between them also increases. Since Newtonian mechanics can be derived. which includes pieces that have won the mass of the earth is so much Once you add to that the inventive him international awards and acclaim forms, surfaces and objects reacting greater than everyday objects, and from his peers in the juggling the distance from the center to the together included within this show and community. And in this Study Guide, surface of the earth is approximately a whole array of lessons is covered in take in some of the concepts that brief. Here is a partial list of just some the same anywhere on the earth’s have guided his work. surface, differences in an object’s of the concepts utilized in the mass and height become negligible. performance: About Greg (the Bio) In an effort to change people's • Gravity Because of this, the acceleration of gravity on everyday objects here on preconceptions about juggling, Greg • Angle of Rebound earth is constant and predictable! Kennedy fuses logic and creativity to • Elliptical Movement synthesize new forms of juggling • Pendulum Movement manipulation. In the early 1990's, • Centripetal Acceleration Greg spent several years working as • Gyroscopic Stability a professional engineer, in addition to • Light Refraction his juggling career. His fascination • Spectral Dispersion with the geometry and physics of object manipulation led him to As you can see this program touches ground-breaking work with original on most concepts of a first year apparatus, expanding the realm of Physics course. The performance can juggling. "He is a visionary who can simply be viewed as live demonstra- see the possibilities in props and tion of physical properties. movement that are obscure to the masses," writes Bill Giduz, Jugglers World magazine. Wow, that seems really complex, no An ellipse can be approximated by wonder it is so hard to juggle! rolling a ball on the inside surface of a Actually, all the math simply states sphere. Depending on the ball’s the opposite. Although it may look initial speed and direction, the ellipse really confusing, what all those varies in eccentricity. A ball rolled numbers mean is that an object which quickly to one side at the rim will have is thrown acts in a predictable a low eccentricity being very close to manner. What goes up, must come a circle. One rolled only slightly to down! the side will have a very high eccentricity and be oblong. How does this affect my juggling? I can predict the position time and speed of exactly how the balls will fall It uses two rigid surfaces placed in a back down, and how they will travel in V-shape 90 degrees from one another the air when I throw them. This and each 45 degree angles from the enables me to track multiple objects ground. Multiple balls are bounced off in the air, creating many different the surfaces, creating different visual types of juggling patterns. patterns. Sometimes I juggle different objects I used the physics above to help me of different masses, but they still all create my routine, predicting how the accelerate back down at the same balls would travel upon collision with rate. Do you know why? the surfaces. An interesting aspect of this shape is that when I throw a ball Angle of Rebound straight down one foot right of center, In 1995 I started experimenting with Definition after two ricochets it will come straight rolling patterns of multiple objects on Rebound is the reversal in direction of up one foot left of center. Can you the inside surface of a half sphere. I an object upon encountering a predict that with the equation above? was very methodical about barrier. The object approaches along documenting different elliptical paths an angle of incidence and rebounds Elliptical Motion a single ball could travel and then along an angle of reflection. The Definition using mathematics to derive different angle of incidence, θi is the angle An ellipse is an oval. At any point on patterns which were possible with measured from the incoming direction the arc, the sum of the distances to multiple balls, not all of which I was of the object to a line drawn normal two distinct focus points is always the able to learn. (90 degrees) from the surface. The same. Johannes Kepler developed angle of reflection, θr is the angle laws which described the motion of I spent hundreds of hours over the measured from the line drawn normal the planets across the sky. He next year developing a routine. I to the surface to the outgoing showed that all planets move in found that using the surface gave me direction of the object. elliptical orbits, with the sun at one much more control than traditional focus. toss juggling and enabled me to do Equation many more objects (up to ten), but in The law of reflection states that the Equation such a small space collisions are angle of reflection and angle of Every ellipse has an eccentricity, e common. Do you think it’s easier to incidence are equal. which describes how elongated it is eliminate collisions with high eccen- and how far apart the two focus point tricity ellipses or low eccentricity θr = θi are. The eccentricity of an ellipse ellipses? Why? (ranging from 0 to 1) can be defined Because of this, one can accurately as the ratio of the distance between Simple Pendulums predict how a ball will rebound from a the foci, C to the major axis of the Definition surface based on the angle at which it ellipse, A. The eccentricity is zero for A simple pendulum is a weight approaches. To change where the a circle and near one for an elongated suspended from a string or rod of ball will end up, you simply have to ellipse. negligible mass. It has a single change the point which it starts. resonant frequency, which means it e = C repeats its action after a set amount I use these concepts in a bounce ball A of time. It will swing out, then back, routine. I created it after accidentally then repeat itself. breaking a marble slab in half. Equation Centripetal Acceleration The ball stays in contact with the The period T, the time it takes for the Definition track until the velocity is low enough pendulum to repeat itself, of such a Centripetal acceleration describes that the acceleration is lower than pendulum can be approximated in the objects which travel in circular paths. that of gravity. Then they fall out so equation: Newton's laws of motion and law of that I can catch them. If the ball goes ____ gravitation can be used to explain the fast enough, it can continue around T = 2 π \ / L / g circular motion of objects in our solar the circle multiple times before I catch system. While moving in a circular it. where L is pendulum Length, g is the path, an object is constantly being acceleration of gravity, and π is pulled "towards the center" of the The track I use has a 2½ ft radius.