Download Newton`s First Law (Law of Inertia)

Newton’s Laws – Intro to Dynamics
Newton's First Law (Law of Inertia)
Let's restate Newton's first law in everyday terms:
An object at rest will stay at rest, forever, as long as nothing pushes or pulls on it. An object in motion
will stay in motion, traveling in a straight line, forever, until something pushes or pulls on it.
The "forever" part is difficult to swallow sometimes. But imagine that you have three ramps set up as shown below.
Also imagine that the ramps are infinitely long and infinitely smooth. You let a marble roll down the first ramp, which is
set at a slight incline. The marble speeds up on its way down the ramp. Now, you give a gentle push to the marble
going uphill on the second ramp. It slows down as it goes up. Finally, you push a marble on a ramp that represents the
middle state between the first two -- in other words, a ramp that is perfectly horizontal. In this case, the marble will
neither slow down nor speed up. In fact, it should keep rolling. Forever.
Which person in this ring will be harder to move? The
sumo wrestler or the little boy?
According to Newton's first law, the marble on that
bottom ramp should just keep going. And going.
Physicists use the term inertia to describe this 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. To understand how, consider
the sumo wrestler and the boy shown above.
Let's say the wrestler on the left has a mass of 136 kilograms, and the boy on the right has a mass of 30 kilograms
(scientists measure mass in kilograms). Remember the object of sumo wrestling is to move your opponent from his
position. Which person in our example would be easier to move? Common sense tells you that the boy would be easier
to move, or less resistant to inertia.
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.
Interestingly, Newton wasn't the first scientist to come up with the law of inertia. That honor goes to Galileo and to
René Descartes. In fact, the marble-and-ramp thought experiment described previously is credited to Galileo. Newton
owed much to events and people who preceded him. Before we continue with his other two laws, let's review some of
the important history that informed them.
Newton’s Laws – Intro to Dynamics
Newton's Second Law (Law of Motion)
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. This is what it said:
When a force acts on an object, the object accelerates in the direction of the force. If the mass of an
object is held constant, increasing force will increase acceleration. If the force on an object remains
constant, increasing mass will decrease acceleration. In other words, force and acceleration are directly
proportional, while mass and acceleration are inversely proportional.
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:
F = (m)(Δv/Δt)
where the delta (Δ) 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:
F = ma
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/s 2), 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.
So what can you do with Newton's second law? As it turns out, F = ma lets you quantify motion of every variety. Let's
say, for example, you want to calculate the acceleration of the dog led shown below.
Figure 1
Figure 2
Figure 3
If you want to calculate the
acceleration, first you need to modify
the force equation to get a = F/m. When
you plug in the numbers for force (100
N) and mass (50 kg), you find that the
acceleration is 2 m/s2.
Notice that doubling the force by
adding another dog doubles the
acceleration. Oppositely, doubling the
mass to 100 kg would halve the
acceleration to 2 m/s2.
If two dogs are on each side, then the
total force pulling to the left (200 N)
balances the total force pulling to the
right (200 N). That means the net force
on the sled is zero, so the sled doesn’t
move.
Newton’s Laws – Intro to Dynamics
Now let's say that the mass of the sled stays at 50 kg and that another dog is added to the team. If we assume the
second dog pulls with the same force as the first (100 N), the total force would be 200 N and the acceleration would be
4 m/s2.
Finally, let's imagine that a second dog team is attached to the sled so that it can pull in the opposite direction.
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. Now imagine that one of the dogs
on the left breaks free and runs away. Suddenly, the force pulling to the right is larger than the force pulling to the left,
so the sled accelerates to the right.
What's not so obvious in our examples is that the sled is also applying a force on the dogs. In other words, all forces
act in pairs. This is Newton's third law…. Speaking of which!
Newton's Third Law (Law of Force Pairs)
Newton's third law is probably the most familiar. Everyone knows that every action has an equal and opposite reaction,
right? Unfortunately, this statement lacks some necessary detail. This is a better way to say it:
A force is exerted by one object on another object. In other words, every force involves the interaction
of two objects. When one object exerts a force on a second object, the second object also exerts a force
on the first object. The two forces are equal in strength and oriented in opposite directions.
Many people have trouble visualizing this law because it's not as intuitive. In fact, the best way to discuss the law of
force pairs is by presenting examples. Let's start by considering a swimmer facing the wall of a pool. If she places her
feet on the wall and pushes hard, what happens? She shoots backward, away from the wall.
Figure 1
Figure 2
That's one heck of a force!
A baseball player shatters his bat.
Clearly, the swimmer is applying a force to the wall, but her motion indicates that a force is being applied to her, too.
This force comes from the wall, and it's equal in magnitude and opposite in direction.
Next, 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.
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.
Newton’s Laws – Intro to Dynamics
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.
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.
Speaking of outer space, Newton's other laws apply there, too. By using his laws to analyze the motion of planets in
space, Newton was able to come up with a universal law of gravitation. We'll explore this further in the next section
The famous (un)true apple story
Could a falling apple be related to a revolving planet or moon? Newton believed
so. This was his thought process to prove it:
1. An apple falling to the ground must be under the influence of a force,
according to his second law. That force is gravity, which causes the apple
to accelerate toward Earth’s center.
2. Newton reasoned that the moon might be under the influence of Earth's
gravity, as well, but he had to explain why the moon didn't fall into Earth.
Unlike the falling apple, it moved parallel to Earth's surface.
3. What if, he wondered, the moon moved about the Earth in the same way
as a stone whirled around at the end of a string? If the holder of the string
let go -- and therefore stopped applying a force -- the stone would obey
the law of inertia and continue traveling in a straight line, like a tangent
extending from the circumference of the circle.
4. But if the holder of the string didn't let go, the stone would travel in a circular path, like the face of a clock. In
one instant, the stone would be at 12 o'clock. In the next, it would be at 3 o'clock. A force is required to pull
the stone inward so it continues its circular path or orbit. The force comes from the holder of the string.
5. Next, Newton reasoned that the moon orbiting Earth was the same as the stone whirling around on its
string. Earth behaved as the holder of the string, exerting an inward-directed force on the moon. This force
was balanced by the moon's inertia, which tried to keep the moon moving in a straight-line tangent to the
circular path.
6. Finally, Newton extended this line of reasoning to any of the planets revolving around the sun. Each planet
has inertial motion balanced by a gravitational attraction coming from the center of the sun.
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. Distance diminishes this
attraction. Newton expressed this mathematically in this equation:
F = G(m1m2/r2)
where F is the force of gravity between masses m1 and m2, G is a universal constant and r is the distance between the
centers of both masses.
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. But there are two instances where Newtonian physics break down. The first involves
objects traveling at or near the speed of light. The second problem comes when Newton's laws are applied to very
small objects, such as atoms or subatomic particles that fall in the realm of quantum mechanics.