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How Newton’s Laws of Motion Work
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Next to E = mc2, F = ma is the most famous equation in all of physics. Yet many people remain
mystified by this fairly simple algebraic expression. It’s actually a mathematical representation
of Isaac Newton’s second law of motion, one of the great scientist’s most important
contributions. The “second” implies that other laws exist, and, luckily for students and trivia
hounds everywhere, there are only two additional laws of motion. All three are presented here,
using Newton’s own words:
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Every object persists in its state of rest or uniform motion in a straight line unless it is
compelled to change that state by forces impressed on it.
2. Force is equal to the change in momentum per change in time. For a constant mass,
force equals mass times acceleration.
3. For every action, there is an equal and opposite reaction.
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These three laws form the foundation of what is known as classical mechanics, or the science
concerned with the motion of bodies being acted upon by forces. The bodies in motion could be
large objects, such as orbiting moons or planets, or they could be ordinary objects on Earth’s
surface, such as moving vehicles or speeding bullets. Even bodies at rest are fair game.
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A Brief History of Newton’s Laws
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The Greek philosopher Aristotle dominated scientific thinking for many years. His views on
motion were widely accepted because they seemed to support what people observed in nature.
For example, Aristotle thought that weight affected falling objects. A heavier object, he argued,
would reach the ground faster than a lighter object dropped at the same time from the same
height. He also rejected the notion of inertia, asserting instead that a force must be constantly
applied to keep something moving. Both of these concepts were wrong, but it would take many
years – and several daring thinkers – to overturn them.
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The first big blow to Aristotle’s ideas came in the 16th century when Nicolaus Copernicus
published his sun-centered model of the universe. Aristotle theorized that the sun and the moon
and the planets all revolved around Earth on a set of celestial spheres. Copernicus proposed that
the planets of the solar system revolved around the sun, not the Earth. Although not a topic of
mechanics per se, the heliocentric cosmology described by Copernicus revealed the vulnerability
of Aristotle’s science.
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Galileo Galilei was the next to challenge the Greek philosopher’s ideas. Galileo conducted two
now-classic experiments that set the tone and tenor for all scientific work that would follow. In
the first experiment, he dropped a cannonball and a musket ball from the Leaning Tower of Pisa.
Aristotelian theory predicted that the cannonball, much more massive, would fall faster and hit
the ground first. But Galileo found that the two objects fell at the same rate and struck the
ground roughly at the same time.
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Some historians question whether Galileo ever carried out the Pisa experiment, but he followed it
with a second phase of work that has been well documented. These experiments involved bronze
balls of various sizes rolling down an inclined wood plane. Galileo recorded how far a ball
would roll in each one-second interval. He found that the size of the ball didn’t matter—the rate
of its descent along the ramp remained constant. From this, he concluded that freely falling
objects experience uniform acceleration regardless of mass, as long as extraneous forces, such as
air resistance and friction, can be minimized.
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But it was Rene Descartes, the great philosopher, who would add new depth and dimension to
inertial motion. In his “Principles of Philosophy,” Descartes proposed three laws of nature. The
first law states; “that each thing, as far as is in its power, always remains in the same state; and
that consequently, when it is once moved, it always continues to move.” The second holds that
“all movement is, of itself, along straight lines.” This is Newton’s first law, clearly stated in a
book published in 1644—when Newton was still a newborn!
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Clearly, Isaac Newton studied Descartes. He put that studying to good use as he single-handedly
launched the modern era of scientific thinking. Newton's work in mathematics resulted in
integral and differential calculus. His work in optics led to the first reflecting telescope. And yet
his most famous contribution came in the form of three relatively simple laws that could be used,
with great predictive power, to describe the motion of objects on Earth and in the heavens. The
first of these laws came directly from Descartes, but the remaining two belong to Newton alone.
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He described all three in "The Mathematical Principles of Natural Philosophy," or the Principia,
which was published in 1687. Today, the Principia remains one of the most influential books in
the history of human existence.
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Newton’s First Law (Law of Inertia)
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Physicists use the term inertia to describe the tendency of an object to resist a change in its
motion. The Latin root for inertia is the same root for “inert”, which means lacking the ability to
move. So you can see how scientists came up with the word. What’s more amazing is that they
came up with the concept. Inertia isn’t an immediately apparent physical property, such as
length or volume. It is however, related to an object’s mass. You experience inertia in a moving
car all the time. In fact, seatbelts exist in cars specifically to counteract the effects of inertia.
Imagine for a moment that a car at a test track is traveling at a speed of 55 mph. Now imagine
that a crash test dummy is inside that car, riding in the front seat. If the car slams into a wall, the
dummy flies forward into the dashboard. Why? Because, according to Newton’s First Law, an
object in motion will remain in motion until an outside force acts on it. When the car hits the
wall, the dummy keeps moving in a straight line and at a constant speed until the dashboard
applies a force. Seatbelts hold dummies (and passengers) down, protecting them from their own
inertia.
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Newton’s Second Law (Law of Motion)
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You may be surprised to learn that Newton wasn't the genius behind the law of inertia. But
Newton himself wrote that he was able to see so far only because he stood on "the shoulders of
Giants." And see far he did. Although the law of inertia identified forces as the actions required
to stop or start motion, it didn't quantify those forces. Newton's second law supplied the missing
link by relating force to acceleration.
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Technically, Newton equated force to the differential change in momentum per unit time.
Momentum is a characteristic of a moving body determined by the product of the body's mass
and velocity. To determine the differential change in momentum per unit time, Newton
developed a new type of math -- differential calculus. His original equation looked something
like this:
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F = (m)(Δv/Δt)
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where the delta symbols signify change. Because acceleration is defined as the instantaneous
change in velocity in an instant of time (Δv/Δt), the equation is often rewritten as:
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F = ma
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The equation form of Newton's second law allows us to specify a unit of measurement for force.
Because the standard unit of mass is the kilogram (kg) and the standard unit of acceleration is
meters per second squared (m/s2), the unit for force must be a product of the two -- (kg)(m/s2).
This is a little awkward, so scientists decided to use a Newton as the official unit of force. One
Newton, or N, is equivalent to 1 kilogram-meter per second squared. There are 4.448 N in 1
pound.
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This is important because Newton's second law is concerned with net forces. We could rewrite
the law to say: When a net force acts on an object, the object accelerates in the direction of the
net force.
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Newton's Third Law (Law of Force in Pairs)
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Think about a book lying on a table. What forces are acting on it? One big force is Earth's
gravity. In fact, the book's weight is a measurement of Earth's gravitational attraction. So, if we
say the book weighs 10 N, what we're really saying is that Earth is applying a force of 10 N on
the book. The force is directed straight down, toward the center of the planet. Despite this force,
the book remains motionless,which can only mean one thing: There must be another force, equal
to 10 N, pushing upward. That force is coming from the table.
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If you're catching on to Newton's third law, you should have noticed another force pair described
in the paragraph above. Earth is applying a force on the book, so the book must be applying a
force on Earth. Is that possible? Yes, it is, but the book is so small that it cannot appreciably
accelerate something as large as a planet.
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You see something similar, although on a much smaller scale, when a baseball bat strikes a ball.
There's no doubt the bat applies a force to the ball: It accelerates rapidly after being struck. But
the ball must also be applying a force to the bat. The mass of the ball, however, is small
compared to the mass of the bat, which includes the batter attached to the end of it. Still, if
you've ever seen a wooden baseball bat break into pieces as it strikes a ball, then you've seen
firsthand evidence of the ball's force.
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These examples don't show a practical application of Newton's third law. Is there a way to put
force pairs to good use? Jet propulsion is one application. Used by animals such as squid and
octopi, as well as by certain airplanes and rockets, jet propulsion involves forcing a substance
through an opening at high speed. In squid and octopi, the substance is seawater, which is sucked
in through the mantle and ejected through a siphon. Because the animal exerts a force on the
water jet, the water jet exerts a force on the animal, causing it to move. A similar principle is at
work in turbine-equipped jet planes and rockets in space.
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It was a stunning insight -- one that eventually led to the universal law of gravitation. According
to this law, any two objects in the universe attract each other with a force that depends on two
things: the masses of the interacting objects and the distance between them. More massive
objects have bigger gravitational attractions.
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Over the years, scientists in just about every discipline have tested Newton's laws of motion and
found them to be amazingly predictive and reliable.
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