Hello!
In this lecture we'll briefly cover the physics
of motion and energy, including Newton's laws
of motion.
Physics is beautiful.
I know I'm biased, but still, what other subject
allows us to predict the motion of objects
throughout the universe.
Whether it's the throw of a baseball, or the
precision landing of a rover on Mars, we can
use physics to precisely determine where things
will end up.
For example, these two spiral galaxies are
on a collision course.
We can predict the motions of their stars
as the galaxies approach one another over
the next tens of millions of years.
It's pretty neat, right?
I won't spend a lot of time here, but I want
you to obtain some of the basic vocabulary
for describing motion.
First, speed.
The speed of anything tells us how far it
will go in a certain amount of time.
For example, 70 miles per hour is a speed.
If it's the speed of your car, your car will
go 70 miles in one hour.
Velocity tells us both speed and direction.
For example, the boat is going 10 meters per
second, due east.
An object is accelerating if its velocity
is changing.
It's the velocity per time, so the units are
distance per time squared.
You are probably familiar with acceleration
as it applies to increasing speed.
But you are also accelerating if you are turning
because turning changes your velocity - it
changes your direction.
If you are slowing down, you are accelerating
too.
You can often feel the effects of acceleration.
For example, as you speed up in a car you
feel yourself being pushed back into your
seat.
As you drive around a curve you feel yourself
being pushed away from the direction you turn.
As you slow down you feel yourself being pulled
forward from the seat.
In contrast, you don't feel such effects when
you're moving at constant velocity.
One of the most important types of acceleration
is the acceleration caused by gravity.
In a legendary experiment, Galileo supposedly
dropped weights from the leaning tower of
Pisa.
He demonstrated that gravity accelerates all
objects by the same amount regardless of their
mass.
This fact may be surprising because it seems
to contradict everyday experience: a feather,
for example, floats gently to the ground,
while a hammer plummets.
But it's air resistance that causes this difference
in acceleration.
If you dropped a feather and hammer on the
Moon, where there is no air resistance, they
would fall at exactly the same rate.
The acceleration of a falling object is called
the acceleration of gravity, abbreviated 'g'.
On Earth, the acceleration of gravity causes
falling objects to fall faster by about 10
meters per second, with each passing second.
For example, suppose you drop a rock from
a tall building.
At the moment you let it go, its speed is
0 meters per second.
After 1 second the rock will be falling downward
at about 10 meters per second.
After 2 seconds, it will be falling at about
20 meters per second.
In the absence of air resistance, its speed
would continue to increase by about 10 meters
per second each second until it hits the ground.
We therefore say that the acceleration of
gravity is about 10 meters per second per
second, or 10 meters per second squared.
In daily life we usually think of mass as
something you measure with a bathroom scale,
but technically the scale measures your weight,
not your mass.
The distinction between mass and weight is
important in astronomy.
Mass is the mount of matter in an object,
and weight is the force that acts on an object.
Weight is the force that the scale measures
when you stand on it.
To understand the difference between mass
and weight, imagine standing on a scale in
an elevator.
Your mass will be the same no matter how the
elevator moves, but your weight can vary.
When the elevator is stationary or moving
at constant velocity, the scale reads your
"normal" weight.
Now consider an elevator moving at constant
velocity.
In this elevator you will also see your normal
weight on a scale.
If an elevator accelerates upward, the floor
exerts a greater force than it does when you
are at rest.
You feel heavier and the scale verifies your
greater weight.
If the elevator accelerates downward, the
floor and the scale exert a weaker force on
you, so the scale registers less weight.
Remember this only happens when the elevator
is accelerating.
If the elevator cable breaks, the elevator
and you are suddenly in free-fall, falling
without any resistance to slow you down.
The floor drops away at the same rate that
you fall, allowing you to essentially float
freely above it.
The scale reads zero because you are no longer
held to it, and the free-fall has made you
weightless.
You are in free fall whenever there's nothing
to prevent you from falling.
Jump off the table!
You are in free fall, but only for a second.
You've probably seen videos of astronauts
floating weightlessly in the Space Station.
They are weightless, clearly.
But it's not because of a lack of gravity.
There is gravity in space.
They are weightless because they are in free
fall.
Astronauts orbiting Earth are in a constant
state of free fall.
To understand this, imagine a tower that reaches
all the way to the Space Station's orbit.
If you stepped off the tower, you would fall
downward, remaining weightless until you hit
the ground.
We're ignoring air resistance here.
Now, imagine that instead of stepping off
the tower you ran and jumped out of the tower.
You'd still fall to the ground, but because
of your forward motion you'd land a short
distance away from the base of the tower.
The faster you run the farther you go before
landing.
If you could somehow run fast enough, an interesting
thing would happen.
By the time gravity had pulled you downward
as far as the length of the tower, you would
have already moved far enough around the Earth
to notice the curvature of the planet.
That is, as you fall towards Earth, it curves
away from you.
You are in orbit.
The space shuttle, space station, and satellites
are all orbiting Earth because they are constantly
falling.
Here's another way of seeing it.
The Earth's curvature drops a vertical distance
of 5 meters for each 8000 meters tangent to
the surface.
So to orbit Earth, a projectile must travel
8000 meters in the time it takes to fall 5
meters.
We could spend the whole semester talking
about Isaac Newton and his work.
He published his laws of motion and gravity
in 1687 in his book "Mathematical Principles
of Natural Philosophy", or his "Principia".
His laws govern the motion of everything from
our daily movements on Earth to the movements
of stars, planets, and galaxies throughout
the universe.
Newton realized that the same laws that operate
on Earth also operate in the heavens!
And his work completely revolutionized mathematics
and science.
He quantified the laws of motion and gravity,
he conducted experiments regarding the nature
of light, built the first reflecting telescopes,
and he invented calculus.
I want to give you a just brief introduction
to Newton's three laws of motion.
Newton's first law of motion essentially restates
Galileo's discovery that objects will remain
in motion unless acted on by an outside force.
In other words, objects at rest tend to remain
at rest and objects in motion tend to remain
in motion with no change in their speed or
their direction.
A spaceship, for example, needs no fuel to
keep moving in space
Newton's second law of motion tells us what
happens to an object when a net force is present.
This law explains why you can throw a baseball
father than a bowling ball.
Because the mass of the bowling ball is greater,
the same force from your arm gives the bowling
ball a smaller acceleration.
It's just harder to throw something more massive.
Astronomically, Newton's second law explains
why a large planet such as Jupiter has a greater
effect on asteroids and comets than a smaller
planet such as Earth.
Because Jupiter is much more massive than
Earth, it exerts a stronger gravitational
force on passing asteroids and comets, and
therefore can send them scattering with a
greater acceleration.
Are you sitting down right now?
If so, your weight is exerting a downward
force.
If this were the only force, Newton's second
law would demand that you accelerate downward
toward the center of the Earth.
That you are not falling means there must
be no net force acting on you.
The ground must be exerting an upward force
on you that precisely cancels the downward
force you exert on your chair.
The fact that the downward force you exert
on the ground is offset by an equal and opposite
force that pushes upward is an example of
Newton's third law - for any force there is
always an equal and opposite reaction force.
Newton's third law explains how a rocket works.
A rocket engine generates a force that drives
hot gas out of the back, which creates an
equal and opposite force that propels the
rocket forward.
That's all for now.
I know we covered a lot!
So take a break, become a body at rest, and
I'll talk to you again soon.
