Look Out! It’s Momentum!
I’m sure some of my readers have heard about the JATO rocket car, often noted as a Darwin award. You know, that honor awarded to individuals who have self-eliminated themselves through sheer idiocy. The story starts in the 1950s during an episode of the Lawrence Welk show. If you don’t know what that is, I advise you to look it up on YouTube. It’s best enjoyed when you’ve eaten an edible or are enjoying your evening libation or drink. So, back to the episode of the Lawrence Welk show. A commercial about the Dodge Coronet, equipped with JATO units, had aired. The units demonstrated the power of the company’s “total contact” brakes.
This fictional story is born out of that commercial and tells about a man who decided to give his Chevy Impala a turbocharged boost—literally. He just happened to have a JATO unit, an acronym for a Jet-Assisted Take Off unit. Heavy military transport planes typically use this JATO unit for short airfield takeoffs. So, equipped with this unit, this intrepid driver headed into the Arizona desert, where he found a long, straight stretch of road. He then attached the JATO unit to his car and hit the ignition.
The JATO would have reached maximum thrust within five seconds, propelling the Impala to speeds well over 350 MPH, which is also 560 km/h. According to the false story, for 15 to 20 seconds, the car remained on the straight highway for about 2.5 miles before the driver melted the brakes and blew the tires. At this point, he hit a bump and became airborne for 1.4 miles. His grand finale was when he hit the face of a cliff at 125 feet, which left a blackened crater. The story goes on to say that most of the driver’s remains were not recoverable. Still, bone, teeth, and hair fragments were extracted from the crater.
And this is my introduction to the topic of momentum!
How much does a ton of feathers weigh? My dad would always tell me that joke. I don’t know why; I knew the punch line. It weighs a ton. It’s also a great joke when discussing Aristotle’s discoveries. Aristotle believed that heavier objects fall faster than lighter ones. He also thought that a continuous force is required to keep an object in motion. So, for all we know, he might have dropped a ton of feathers from a Cliff to see how fast it fell, but more than likely not. Aristotle did not conduct experiments on momentum in the modern sense. Instead, he formulated theories based on observations and philosophical reasoning. Aristotle’s ideas on motion, which included concepts related to what we now understand as momentum, were part of his broader work in physics.
Aristotle believed that all objects have a natural place in the universe and that they move toward that place. His theories included Natural Motion, wherein he speculated that objects move naturally in straight lines toward their natural places. For example, he noted that heavy objects fall towards the Earth while light objects rise towards the heavens.
He also wrote about Violent Motion, which is the type of motion that occurs when an object is forced to move in a way contrary to its natural motion, such as pushing a rock uphill. Aristotle believed that an external force was needed to maintain this motion. And then there’s the concept of Impetus, which was not fully developed by Aristotle. However, his concept of Impetus suggests that an object in motion carries with it some force that keeps it moving. This idea was later developed by medieval scholars. It can be seen as an early precursor to the modern concept of momentum.
Aristotle’s approach was more qualitative than quantitative, relying on logical reasoning rather than experimental evidence. His theories dominated Western thought until the scientific revolution, when figures like Galileo and Newton used experiments to better understand motion and momentum. Sadly, individuals like Galileo and Newton were ostracized and, worse yet, imprisoned for their findings that opposed the church, which held steadfast to the concepts presented by Aristotle.
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Moving forward in history, we arrive at the Islamic Golden Age from the eighth to the fourteenth century. During this period, scholars in the Islamic world made significant contributions to science and mathematics. One notable figure was Ibn Sina (Avicenna), who believed that a moving object has a force that is dissipated by external agents like air resistance. This idea was an early precursor to the concept of inertia, which is closely related to momentum.
THE RENAISSANCE
However, most of our primary discoveries about momentum come from the Renaissance. Ah, the Renaissance! It was a period of cultural, artistic, and intellectual revival in Europe from the fourteenth century to the seventeenth century. This period was influenced by a range of factors, including political, economic, and social changes. This age saw the rise of wealthy and powerful city-states, such as those in Italy, like Florence, Venice, and Milan. These city-states were ruled by influential families who were patrons of the arts and the sciences and financially supported artists, architects, and scholars. In season three, episode sixty-three, I talk about the mathematical competitions and Tartaglia’s brilliance.
Also, during this time, Constantinople fell, which led to the migration of Greek scholars into Italy, who brought with them classical texts and more knowledge. There was a rise in humanism wherein the intellectual movement emphasized the study of classical texts, individual potential and the importance of human values. People served as political advisers and promoted education and civic responsibility. And this was also the time of the burgeoning merchant class. People had money to play with, so they played with science and math.
As a result, scientists like Galileo Galilei and Sir Isaac Newton made discoveries that revolutionized our understanding of momentum and motion. I talk extensively about Galileo in season three, episodes fifty-seven and fifty-eight, if you want to learn more about his inquisition. He is often referred to as the “father of modern science” and conducted experiments that challenged Aristotelian physics. He observed momentum by conducting experiments with inclined planes and pendulums. In doing so, he demonstrated that the velocity of falling objects is independent of their mass. He also introduced the concept of inertia, stating that an object in motion remains in motion unless acted upon by an external force.
These ideas culminated with Sir Isaac Newton, whose work laid the foundation for classical mechanics. Newton formulated three laws of motion, with the first law of motion stating that a body in motion remains in motion or a body at rest remains at rest unless acted upon by a force. His second law states that the force acting on an object is equal to the rate of change of its momentum, and the third law states that for every action, there is an equal and opposite reaction. It is his second law that is most fundamental to the concept of momentum. I’ll just state it again for kicks, his second law states that the force acting on an object is equal to the rate of change of its momentum.
This law of motion defines how objects move when forces act on them. For example, when you push or pull an object, you apply a force to it. The speed at which an object moves, its acceleration, depends on the net force that acts on it. For example, imagine that you have a toy car. The harder you push the toy car, the faster it accelerates.
Newton’s second law is mathematically expressed as acceleration equals the net force divided by the object’s mass. Newton’s second law can be expressed mathematically as:
a=\frac{\Sigma f}{m}Wherein a represents acceleration, Sigma f is the net force acting on the object in all directions, and m is the mass of the object.
What this means is if you double the net force, the acceleration of the object doubles as well. Also, if you double the mass, the acceleration is halved. For example, when the same force is applied, lighter objects accelerate more easily than heavier ones. So, let’s say you need to move a filing cabinet across the room. If you empty the filing cabinet before you push it, it will move more easily than if you push it across the room with all the files in it. And this is a real case scenario because I was just reorganizing my office the other day!
NINETEENTH CENTURY AND BEYOND
The nineteenth century witnessed further advancements in the study of momentum, particularly with the development of the conservation laws. The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act upon it. This principle is a direct consequence of Newton’s laws and has far-reaching implications in various fields.
Within this definition, there are two key types of momentum conservation. The first is linear momentum conservation, and the second is angular momentum conservation.
In linear momentum conservation, like a collision, the total linear momentum before an event equals the total linear momentum after the event. With angular momentum conservation, in an isolated system, the total angular momentum remains constant if no external torques are acting on it.
So, let’s imagine two cars colliding head-on and coming to a stop. Before the collision, both vehicles are moving with specific velocities. According to Newton’s third law of motion, the forces each car exerts on the other are equal in magnitude and opposite in direction.
Linear Momentum Conservation states that the system’s total momentum (both cars together) remains constant if no external forces act on it. In this case, the only external force might be friction with the road, which is usually negligible in such a short timeframe.
So, before the collision, the total momentum of both cars combined (considering their masses and velocities) is equal to the total momentum after the collision, where they come to a stop.
Angular Momentum Conservation refers to the rotational motion of an object. In the context of a car accident, let’s consider the wheels of the cars spinning before and after the collision.
When the two cars collided, before the collision, their wheels were spinning. Angular momentum is like the spin of a top or a spinning wheel. When the vehicles collide, if there are no external forces making the wheels stop suddenly (like hitting something on the road), the spinning motion of the wheels (angular momentum) would stay the same. This means that the total “spin energy” in the wheels before the collision will be the same as the total “spin energy” after the crash.
So, even though the cars might crash and stop moving forward, their wheels’ spinning motion (angular momentum) remains unchanged unless something external stops them, like hitting a curb.
These conservation laws are crucial in analyzing and predicting the behavior of objects in various physical scenarios, from simple collisions to complex systems in astrophysics.
THE TWENTIETH CENTURY
It is one of my favorite centuries because we talk about Albert Einstein. In the 20th century, Albert Einstein developed the theory of relativity. Relativity introduced significant changes to our understanding of momentum, especially at high velocities approaching the speed of light.
In relativistic mechanics, momentum is defined differently to account for the effects of relativity. As a result, the formula changes because Newtonian mechanics no longer accurately describes momentum because velocities are substantial fractions of the speed of light.
Mathematically, relativistic momentum is defined as:
p=\gamma m v
where:
p is the relativistic momentum,
γ (gamma) is the Lorentz factor, which is
\gamma=\frac{1}{\sqrt {1- \frac{v^2}{c^2}}}m is the rest mass of the object,
v is the velocity of the object,
c is the speed of light in a vacuum wherein (c≈3×108 meters per second).
This application ensures that the laws of physics, including the conservation of momentum, hold true in all reference frames.
QUANTUM MECHANICS AND MODERN PHYSICS
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As the 20th century progressed, the development of quantum mechanics further enriched our understanding of momentum. In quantum mechanics, momentum is described as an operator that acts on the wave function of particles. Louis de Broglie introduced his hypothesis that introduced the concept of matter waves, which states that particles like electrons exhibit particle-like and wave-like properties. This duality is essential in understanding phenomena at the atomic and subatomic levels. However, we can’t quite understand the phenomena until we look at Werner Heisenberg’s uncertainty principle, which states that a particle’s position and momentum cannot be precisely determined simultaneously. This principle has profound implications for our understanding of the behavior of particles at the quantum level. It highlights the probabilistic nature of quantum mechanics.
In the de Broglie hypothesis, let’s imagine small particles, like electrons, behaving not just as tiny balls but also as waves. The de Broglie hypothesis suggests that each particle has a corresponding wavelength, similar to how light or sound waves have wavelengths. The wavelength depends on the particle’s speed, which is momentum.
Now, because particles have this wave-like nature, we can’t pinpoint their exact location and speed (aka momentum) simultaneously. Heisenberg’s Uncertainty Principle tells us that when we precisely know one of these things (like where a particle is), the less accurately we can know the other (like how fast it’s moving).
APPLICATIONS OF MOMENTUM IN VARIOUS FIELDS
Momentum is not just a theoretical concept confined to physics textbooks; it has practical applications in various fields. In space exploration, momentum plays a crucial role in the movement and control of spacecraft. The conservation of momentum is utilized in maneuvers such as slingshot techniques, where a spacecraft gains momentum by passing close to a planet, effectively “stealing” some of the planet’s momentum.
In engineering, understanding momentum is essential for designing vehicle safety features, such as position of airbags and crumble zones. These features are designed to manage the forces and momentum during collisions, reducing the impact on passengers and increasing safety.
In sports, momentum is a critical factor in the performance of athletes. Whether it’s a football player transferring momentum to the ball during a kick or a gymnast using their momentum to execute a flip, understanding and controlling momentum can make a significant difference in performance.
In finance and economics, momentum investing is a strategy where investors buy securities that have performed well in the past, betting that they will continue to do so. This strategy is based on the idea that positive trends in momentum can persist, similar to how momentum works in physics.
Momentum has also made its mark in popular culture, often being used metaphorically to describe situations where there is a build-up of energy or force that drives events forward. Whether in movies, sports commentary, or everyday language, momentum resonates with people as a powerful force that can shape outcomes.
As we look to the future, the study of momentum continues to evolve. Advances in technology and experimental techniques are allowing scientists to explore momentum at even smaller scales and higher energies. The development of particle accelerators, such as the Large Hadron Collider, enables researchers to probe the fundamental properties of particles and their interactions, deepening our understanding of momentum in the process.
Additionally, the exploration of dark matter and dark energy, which make up the majority of the universe, presents new challenges and opportunities for the study of momentum. Understanding how these mysterious components of the universe interact with regular matter and influence cosmic momentum is an exciting frontier in modern physics.
From ancient Greek philosophers to modern physicists, the concept of momentum has evolved and expanded, influencing a wide range of fields and applications. Understanding momentum enhances our comprehension of the natural world and provides practical insights that impact our everyday lives. But of all the concepts I talked about, there is one type of momentum I have not mentioned yet, and it’s the most valuable concept of all. It is that momentum that lives in our hearts.
Sometimes it could be a subject matter that we absolutely adore and can’t get enough of, in my case, the history of math and science. Sometimes, it could be your favorite dessert. There’s momentum within you to buy it and enjoy every bite. Sometimes, it could be a human you adore and want to spend the rest of your life with. You are pulled to them with some invisible force. Other times, it could be a lost pet that someone abandoned, and you end up adopting it and loving it unconditionally. And then there’s the momentum that drives us to help others, to give to charities, and to devote our time and our lives to ensuring the well-being of others. This momentum in our hearts drives us to be better humans, putting our conscience and humanity first. Some may think that momentum is love, but to me, that’s not just love; that is physics. Beautiful, incredible, impactful (pun intended) physics. We are like the stars in the sky that swirl to the momentum of gravity and the subatomic particles that are attracted or repelled by external forces. We are part of this beautiful Dance of momentum that the universe has created. That said, here is to the momentum that resides in your hearts! Until next time, carpe diem, my friends!