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♪♪
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Nice shot, Tom.
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(sighs)
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Ooh, mine, not so much.
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Seems like the momentum of
my ball got lost, or did it?
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Pool is a game
of real skill,
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and it's also
a way to look at
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one of the most powerful
laws of physics.
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We'll find out how
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in this segment of
"Physics in Motion,"
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as we look at the law of
the conservation of momentum.
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During this series,
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we'll talk about
a few conservation laws,
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specifically for energy,
momentum, charge, and mass.
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These fundamental
quantities
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cannot be created
or destroyed.
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They can only be changed
from one form to another,
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or transferred from
one object to another.
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So, what do you think
happens to the momentum
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of billiard balls when
they strike another ball?
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If you figured that the
momentum is conserved,
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you're right.
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The law of the conservation
of momentum says that
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in a collision
between objects
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in a closed and
isolated system,
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the total momentum of
the objects in the system
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before the collision is
equal to the total momentum
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of the objects in the system
after the collision.
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Just like the other
laws of conservation,
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momentum is not
created or destroyed.
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There's another law of physics
that might sound familiar
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when we talk
about collisions.
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Remember Newton's laws,
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which predict the motion
of most objects?
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His third law of
motion states
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that for every action,
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there is an equal
and opposite reaction.
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This means that objects
exert equal forces
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on one another
when they interact.
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One of the consequences
of Newton's third law
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is the law of
conservation of momentum.
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We can see it in action
when you hit a straight shot,
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like this,
and it does this.
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You exert a force
on the cue ball,
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which makes it
gain momentum.
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When you strike the ball,
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that momentum is
transferred to it.
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When the ball collides
with the other ball
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and the first ball stops,
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all the momentum has
been transferred
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from the first ball
to the second ball.
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But what about
in this case?
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This time, the cue ball hits
the other ball at an angle,
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and both balls
are moving.
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So, was the momentum
conserved?
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If you answered yes,
you're right.
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Remember that momentum,
like velocity and direction,
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is a vector quantity.
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When the first ball
travels in this direction,
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it carries some of
the momentum with it.
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The rest is transferred
to the second ball,
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but not enough to
reach the pocket.
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However, none of
the momentum was lost,
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only transferred.
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In equation form, we see
that the total momentum, P,
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before objects interact
with one another,
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is equal to the total
momentum of all the objects
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after they interact.
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Now, ready to try
solving a problem?
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A pool player is about
to use the cue ball
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to make a direct hit
on the eight ball,
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which is at rest.
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Each ball has a mass
of 170.0 grams,
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and the cue ball's
initial speed
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is 6.00 meters
per second.
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After the collision, the
cue ball comes to a stop.
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If no momentum is lost
in the collision,
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what is the total
momentum of this system,
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and how fast is the eight ball
moving after the collision?
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Remember, the momentum
of an object
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is equal to its mass
times its velocity.
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P equals M times V.
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The unit for momentum is
kilogram meters per second.
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To be consistent, we'll convert
the mass to kilograms.
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The cue ball has a mass
of 0.170 kilograms.
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So, let's multiply
that by the velocity
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of 6.00 meters
per second.
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So, the momentum of the
cue ball before the collision
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is 1.02 kilograms
meters per second.
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Since objects at rest
do not have momentum,
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the eight ball begins
with zero momentum.
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So, the total momentum
of the cue ball
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and the eight ball together
before the collision
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is also 1.02 kilograms
meters per second,
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and because momentum
is conserved,
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1.02 kilograms
meters per second
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is the system's total momentum
after the collision, too.
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Now, what about the final
velocity of the eight ball?
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Since the collision brings
the cue ball to rest,
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the eight ball carries
all the system's momentum.
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That means we can divide 1.02
kilograms meters per second
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by 0.170 kilograms,
the eight ball's mass,
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to find its velocity,
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and that turns out to be
6.00 meters per second,
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the same as the cue ball
had at first.
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See how the law of
conservation of momentum
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helped us solve
this equation?
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You apply the law of
conservation of momentum
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only when a collision
happens in a closed,
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isolated system.
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That means
matter and energy
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do not enter or
leave the system,
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which means there are
no net outside forces
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acting on the system.
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In our example, the two
pool balls are the system.
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They don't enter or leave,
so the system is closed.
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The only force
we consider
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is the force between the
two balls when they collide.
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We're not concerned about the
initial force of the cue stick
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or the friction between
the balls and the table.
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So we say that
the system is isolated.
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♪♪
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Let's do one more where we can
look at speed and direction,
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but this time, we'll do it
while roller skating.
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We have two people
facing each other.
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Chirag is 60.0 kilograms,
and Summer is 45.0 kilograms.
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Both are at rest.
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Okay, so, put your
hands together.
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Now, push.
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Chirag is moving
in one direction
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at a speed of 2.00
meters per second.
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What is Summer's
speed and direction?
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We're doing this
mathematically, remember.
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First, we establish
their initial momentum.
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That would be zero
because they're at rest.
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The final momentum
of the system
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will be the sum of the momentum
values for Summer and Chirag,
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which are equal to their mass
times their final velocity.
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If the total initial momentum
of the system is zero,
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the total final momentum
of the system
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must also be zero.
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So, we know that Chirag
and Summer must have equal
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and opposite momenta.
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Now, let's substitute the
mass of Chirag and Summer
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in our values and
Chirag's final velocity
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to determine Summer's
final velocity.
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We know that Summer's mass
is 45.0 kilograms.
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Chirag's mass is
60.0 kilograms,
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and his final velocity is
2.00 meters per second.
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The only other value
in the equation
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is Summer's
final velocity,
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which is what
we're solving for.
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We multiply Chirag's mass
times his final velocity
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to get a final momentum
of 120.0 kilograms
meters per second.
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Remember, the sign indicates
the direction of motion
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of Chirag and Summer.
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And because they're moving
in opposite directions,
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they should have
opposite signs.
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We divide both sides
by 45.0 kilograms
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to get Summer's
final velocity,
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and that turns
out to be
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negative 2.70
meters per second.
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So, let's check.
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Does this answer
make sense?
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Does the sign in front
of Summer's velocity
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represent the direction
of her motion
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compared to the
direction of Chirag?
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And secondly, does the
value of Summer's speed
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compare reasonably to the
value of Chirag's speed?
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The answer to both of
these questions is yes.
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Chirag's had a final
velocity of positive
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2.00 meters per second,
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and Summer's was negative
2.70 meters per second.
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The sign indicated the
direction of motion,
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and when they pushed
off of one another,
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they moved in
opposite directions.
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We see the conservation
of momentum at work
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all around us.
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When you step onto
a dock from a boat,
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you push forward,
and the boat moves backward.
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When you shoot an
arrow at a target,
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the recoil of the bow
has the opposite
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and equal momentum
of the arrow.
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And when you
launch a rocket,
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the exhaust pushes it forward
in equal and opposite measure,
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sending it out of
the earth's atmosphere
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with power and precision.
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Conservation laws,
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including the
conservation of momentum,
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are vital in physics
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because they make it
possible to predict
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how a system
will behave
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without having to
consider every detail.
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Once you know a few things
about the initial condition,
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you can say a lot about
the final state of a system.
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For more practice
with momentum,
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check out our
Closer Look.
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That's it for this segment
of "Physics in Motion,"
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and we'll see you
guys next time.
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For more practice
problems,
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lab activities,
and note-taking guides,
00:09:30
check out the
"Physics in Motion" toolkit.
