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Edwin Robles Jr.
Professor Dominguez
PHYS 440
8 May 2015
Biomechanics in Hip-Hop Dance
Introduction:
When it comes to dance, one may think of it as solely an art form or genre of
dance where conversational and expressive movement is executed to convey meaning or
a message. However, we can set aside the artistic perspective of it and analyze the
movement aspect of it scientifically. For the focus of this research paper, I have looked
upon the biomechanics of a sub-genre in the dance world; Hip-Hop Dance. To fully
assess such a topic of interest, we need to identify the origins of each topic. First, we will
start off with Hip-Hop Dance and the culture behind it and then continuing on into the
development, study, and origins of Biomechanics. Lastly, before analyzing the scientific,
physical analysis of fusing the two ideas together, the motivations and main points of this
topic will be looked upon.
Also loosely known as Urban Dance or Street Dance (due to it’s evolving nature
taking some movement from other forms of dance such as ballet, jazz, modern, and
contemporary), this art originated as breakdancing or Bboying, and was brought along
with the uprising of DJing, MCing or Rapping, and Graffiti as one of the four main
elements to the Hip-Hop culture. The 1970’s brought a significant impact in society when
the founding fathers of Hip-Hop such as DJ Kool Herc, Afrika Bambaataa, Grandmaster
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Flash, and several others released music tracks which consisted of rhythmic beats
accompanied by vocals in which the artist would express words in rhyme form, known as
rapping or MCing. Hip-Hop Dance itself would accompany these musical tracks as an
expression to what these musical artists would rap about. With its origins of being
discovered in the Bronx of New York City, the Hip-Hop culture itself has evolved
through time and will continue to change in the present and for the future.
Biomechanics first came about when the ideas of Aristotle wrote one of the first
books titled, “De Motu Animalium” (meaning the movement of animals). In it, Aristotle
had figures and diagrams of different animals looking at the way in which the science of
movement within these species could be proven as. Therefore, the study of biomechanics
could be defined as the knowledge of movement for biological organisms applying the
laws and principles of physics. For example, one could identify the motion and physics
behind a pitcher throwing a baseball, or even the flight of birds.
With both ideas intact, this brings me now to the actual topic of this paper;
Combining the two ideas of Hip-Hop Dance along with biomechanics to seek meaning
and understanding movement of the body with dance as well as applying the laws of
Physics to it. In particular, Newtonian Mechanics will play a vital role in this exploration.
The main reason as to why I decided to research such a topic as this is because I have
been a dancer since I was eight years old when I took my first Hip-Hop Dance class.
From there, I have competed and performed at various shows throughout the country and
other places such as Germany and Australia. I have taught Hip-Hop Dance at several
locations throughout San Diego County and hope to continue to as a hobby as I look
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towards the future in a Physics-based career. Included in this paper, I have looked at
subtopics and ideas within dance where the physical principles of Newtonian Mechanics
can be applied such as balance, acceleration from rest, motions of turning, and the effects
of body size within dance. There is also an experimental analysis where I was able to
analyze and compare the moment of inertia of different turns in dance, which, ultimately
leads to conclusions of turning velocity and and angular momentum. Now, this leads me
then into the ideas of balance and how your body reacts when movement is applied.
Body/Experimental Analysis:
As defined in Physics and the Art of Dance written by Kenneth Laws (2002), your
center of gravity is “that point where the downward force of gravity appears to act on the
body as whole” (p. 20). For woman, it is most common in the hips in women due to a
greater hip mass as in men, it is located in the chest and shoulder areas. This center of
gravity in humans cannot be moved from rest unless another net force acts on the body as
a whole. For example, let us examine a figure in which a man is standing in place,
represented by a Free-body diagram, where forces can be seen quantitatively as vectors
(Figure 1). Here, we notice that first two laws of Newtonian Mechanics can be applied, in
which case as told by Laws (2002), “In the absence of any interaction with the rest of the
universe, a body will either remain at rest or move in a straight line with a constant
Figure 1: Free-body
diagram with Newton’s
2nd Law Applied.
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velocity” (p. 188) as well as “If a force F is applied to a body of mass m, the resulting
acceleration a is given by a = F/m” (p. 188). Figure 1 satisfies both of these laws and can
be seen by calculating the net force (in this case, FNET = 0 since the body has an
acceleration rate of 0) upon the body. The sum of forces within this figure can also be
seen as equaling zero. In a perfect world, we could remain motionless. However, due to
the nature of our bodies continuously breathing and our consistent heartbeat, our balance
is continuously shifting. In order for us to sustain our balance, during movement or if
stationary, the area of support on the floor must be relocated to fall directly under the
center of gravity or, vice versa. Now, applying this to movement and dance, this can be
seen when a dancer starts out with their legs shoulder width and hands to the side before
a section of movement is executed. It is possible to still contain your center of balance
between your feet as well by isolating movement with just the arms. When shifting
weight from side to side but remaining in place where horizontal movement only takes
place of the upper body, your center of balance changes slightly and very little, which
allows you to still keep in contact with the floor without falling due to a stable position
(seen in Figure 2).
Now, for example, say you lift your foot up and you are trying to execute
movement of the upper body while keeping one foot in contact with the floor. Over time,
your center of gravity will need to find a way to keep your balance without falling. Figure
Figure 2: Center of gravity
on the body of a figure.
(Center of gravity differs
between both males and
females.
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Figure 3: The other forces applied to the body as you try to find
your center of balance or gravity.
3 shows a figure showing that the center of supporting force is needs to be controlled
over time. Although there are other forces pulling and pushing your body, by allowing
your weight to switch between your heal and toe on the supporting leg, your center of
gravity can keep your body to hold a certain move or position. Therefore, if your center
of gravity is not kept intact, your body will result in losing balance concluding in a fall or
motion that will take you out of your stationary state.
This leads me into my next idea in presenting the ideas of acceleration from rest.
Newton’s third law in classical mechanics states that “if object 1 exerts a force on object
2, object 2 must also exert an equal and opposite force on object 1” (Zimba, 2009, p.
283). Acceleration can be seen as the rate of change in velocity of an object. Whether,
that involves a decrease or increase in speed or change in the direction of motion, this
allows dynamics to happen in dance. When a dancer is able to provide rapid movement to
slow paced movement, a dynamics occurs. To allow acceleration to take place in a set of
movement from a starting position, the center of force between the feet and the floor must
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be shifted. If one would like to travel in a forward direction, one must push off the floor
to achieve a displacement in position. As with classical mechanics, we know that
position, velocity, and acceleration are all directly related to one another. If we let some
position equal xi as a function of time, we can treat that position as xi(t). If the object is
displaced and is then at a new location, labeled as xf(t), position can then be seen as a
displacement x(t). Now looking for the velocity of the position we can take the derivative
of that displacement which results in dx/dt, as that is true in that velocity describes the
rate of change in position. After all, it’s units convert from some distance to distance over
time. With acceleration, this can then be found by taking the derivative of the first
resulting in d2x / dt2. Moving forward, to obtain a good increase in acceleration with
movement, one must start in a lunge-like position. This causes the back foot to feel a
push against the floor if one wants to change their position in a horizontal motion.
Compared to a starting position where you are in an upright position where your feet start
close together, your center of gravity will not be able to shift as far forward or backward
resulting in a lower rate of acceleration. This makes sense as to why professional athletes
and runners start a race in the lunged position; to obtain a greater acceleration. With a
Figure 4: A dancer starting in a lunge vs. starting with feet together.
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position such as this, your center of gravity is far forward of the supporting feet when
your hands lift off the ground, which in return, causes an exerting accelerated force with
your feet. Figure 4 shows exactly this; a dancer starting in a lunge vs. a dancer starting
with feet together. This type of movement is examined in order to execute an efficient
turn, since the body is put in motion.
The third concept I want to look at with the biomechanics of Hip-Hop Dance
involves the ideas of rotational momentum and torque. This ultimately leads to the
movement of turning in dance. Torque can be defined as a force that causes a rotation.
Previously, I discussed the idea that in order to achieve efficient acceleration, one must be
in a lunge-like acceleration. This not only holds true for horizontal movement, but as well
as for torque. Figure 5 shows two types of diagrams in which torque can be seen in the
body with movement. We know that in order to obtain a value for torque, the elementary
equation for it is stated as T = F x d, where T represents torque, F represents the force
pair of whatever object is spinning and d acts as the distance between the two force pairs.
This proves the idea that the closer your feet are together, the smaller your torque you are
able to have.
Figure 5: birds eye
view of a dancer’s
foot position with
torque involved.
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Rotational momentum is the quantity in which it is a value relative to rotational
motion. Mathematically, we use the equation L = I x ω. L represents rotational
momentum, I refers to it’s rotational inertia, and ω refers to it’s turn rate, or rotational
velocity. Rotational inertia itself is the value that increases or decreases when a mass is
farther from the rotation axis. Similarly, the basic equation we know from classical
mechanics is that momentum is p = m x v, where p represents momentum, m represents
mass, and v represents the velocity. Comparing these two equations, it makes sense that
these two are both similar. If we look at the units acted upon both momentum and rational
momentum, they are similar (mass x velocity), which indeed makes sense.The only
difference is the fact that rotational momentum measures the value at which an object
rotates rather than measuring the momentum obtained traveling at a horizontal distance.
For our case, the rotational inertia can change between two states; either when the arms
are out and extended to the side or when they are tucked parallel to the body. The
rotational momentum of a dancer is greatest when the legs and arms are extended to the
side than when they are close together to the body. This then must mean that the turn rate
of the mass is smaller. These two values are inversely proportional to one another.
Therefore, if the arms and legs are closer to the body, the rotational velocity increases,
providing a smaller rotational momentum compared to turning with extended arms which
will result in a greater rotational momentum, but smaller turn rate. Ultimately, this makes
sense and can be seen when analyzing two different dancers; specifically an adult and
child. In an adult, because our mass is larger, the turn rate for us is not as efficient as it
would be seen in a child who has a smaller mass. However, the adult would have greater
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power in looking at the rotational momentum carried with the turn compared to a child,
who would in return, have less. Therefore, the resultant rational momentum given by both
dancers is stored, in which the quantity obtained remains constant when no other torques
act upon the body during a turn.
Now, one might ask, “How do I turn faster mid-turn?” Say you wanted to change
the rate of your turn to an increased speed when already establishing rotational
momentum. The trick to this is to start with your arms out fully extended to the side and
as your rotational momentum starts to decelerate due to a loss in torque, you can whip
your arms in towards your body to obtain one last turn. Something to note is that angular,
or, rotational momentum is conserved. Mathematically, this can be proven with looking at
Figure 6: Experimental analysis looking at the different cases of a turn when dancing.
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moments of inertia within the body. Experimental analysis was done for this paper
(Figure 6) to show that tucking in arms will provide a lower moment of inertia with a
greater ω (turn rate) while a higher moment of inertia will provide a smaller value of ω.
As given by the results, I personally have a moment of inertia of 2.3861 kg x m2 when
my arms are fully extended during a given turn and then contract to 1.289 kg x m2 when
my arms are tucked in during a turn. The moment of inertia values were calculated
through sets of formula from Laws (Physics and the Art of Dance) and Winter
(Biomechanics and Motor Control of Human Movement). Assumptions made during this
experiment were to analogize the human body as a cylinder and the arms extended as
rods rotating around a fixed plane (the body acting as the plane).
Conclusions/Reflection:
In conclusion, the biomechanics in Hip-Hop dance are similar to those of everyday
movement in the human body. The ideas and laws of Newtonian Physics play a vital role
in executing movement as well as dynamics to help convey a powerful art form. Similar
mechanics in this paper can be seen in other genres of dance as well including ballet,
modern, contemporary, and tap. We looked at the role of balance and center of gravity in
the body, how acceleration plays a role in horizontal movement, and the rotational
momentum and torque acted out in this system during the movement of turns. Overall,
this paper and research really enhanced my knowledge as a dancer and future physicist,
as it allowed me to explore a hobby of mine and learn classical mechanics behind it as
well. If given more time, I would definitely look at the mechanics of other types of
movement in other genres of dance and conclude to a quantitative experiment in which I
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am able to measure my own momentum, acceleration and other applications of physics
given involved in a series of horizontal movement. Also, I would compare the process of
calorimetry with dance itself and compare it with other forms of dance (comparing the
calories burned between genres). For example, figuring out how much a dancer needs to
eat in order to not exhaust himself or herself would be crucial information to the dance
community and physicists to expand knowledge of how biomechanics work in this type
of growing art form.
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Works-Cited
Laws, K. (2002). Physics and the Art of Dance. New York, NY: Oxford University Press.
Winter, D. (2005). Biomechanics and Motor Control of Human Movement 3rd Edition.
Hoboken, NJ: John Wiley & Sons, Inc.
Zimba, J. (2009). Force and Motion : An Illustrated Guide to Newton's Laws. N.p.: Johns
Hopkins University Press. Retrieved from ProQuest.