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Lecture Outline
Chapter 6
College Physics, 7th Edition
Wilson / Buffa / Lou
© 2010 Pearson Education, Inc.
Chapter 6
Linear Momentum and
Collisions
Linear Momentum
Impulse
Conservation of Linear Momentum
Elastic and Inelastic Collisions
Center of Mass
Jet Propulsion and Rockets
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Momentum
• Brainstorm at least 9 things about
Momentum
–
–
–
–
These can include examples.
A definition
Real World Applications
Etc.
6.1 Linear Momentum
• Newton referred to Momentum as “the
quantity of motion arising from velocity and
the quantity of matter conjointly.”
• Newton’s Second Law was really with
momentum instead of acceleration! HOLY
CRAP!
6.1 Linear Momentum
Definition of linear momentum:
The linear momentum of an object is the product of
its mass and velocity. [For a single particle]
Note that momentum is a vector.
SI unit of momentum: kg • m/s. This unit has
no special name.
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6.1 Linear Momentum
For a system of objects, the total linear
momentum is the vector sum of each.
Find the momentum for each particle or object
and then add them all up! 
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Question 6.2a Momentum and KE I
A system of particles is
known to have a total
kinetic energy of zero.
What can you say about
the total momentum of
the system?
a) momentum of the system is positive
b) momentum of the system is negative
c) momentum of the system is zero
d) you cannot say anything about the
momentum of the system
Question 6.2c Momentum and KE III
Two objects are known to have
the same momentum. Do these
a) yes
two objects necessarily have the
b) no
same kinetic energy?
6.1 Linear Momentum
• A 100 kg football player runs with a velocity of 4
m/s straight down the field. A 1.0 kg artillery shell
leaves the barrel of a gun with a muzzle velocity
of 500 m/s. Which has the greater momentum, the
football player or the shell?
6.1 Linear Momentum
• Conceptual Question: Consider the
following: a .22 caliber bullet, a cruise ship,
and a glacier. Assuming each to be moving
at its normal speed, which would you
expect to have the greatest linear
momentum?
6.1 Linear Momentum
The change in momentum is the difference between
the momentum vectors.
The vector sum and the vector difference are
different!
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6.1 Linear Momentum
6.1 Linear Momentum
• In the object changes velocity, then that
means it must be _____________.
• If something is accelerating, that means this
must be acting on it ______________.
• Similarly, momentum is directly related to
velocity.
• Therefore, a change in momentum also
requires a net force.
6.1 Linear Momentum
If an object’s momentum changes, a force
must have acted on it.
The net force is equal to the rate of change of
the momentum.
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Question 6.3a Momentum and Force
A net force of 200 N acts on a 100-kg
boulder, and a force of the same
magnitude acts on a 130-g pebble.
How does the rate of change of the
boulder’s momentum compare to
the rate of change of the pebble’s
momentum?
a) greater than
b) less than
c) equal to
6.2 Impulse
Impulse is the change in momentum:
When two objects collide they can exert a
large force on one another for a short
period of time. This is called Impulse!
S.I. Unit of Impulse is N s
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6.2 Impulse
• An impulse exerted on an object is equal to
the change in the objects momentum.
• This is called the Impulse – Momentum
Theorem
– Similar to Work – Energy Theorem
Question 6.7 Impulse
A small beanbag and a bouncy
rubber ball are dropped from the
same height above the floor.
They both have the same mass.
Which one will impart the greater
impulse to the floor when it hits?
a) the beanbag
b) the rubber ball
c) both the same
6.2 Impulse
• A golfer drives a 0.046 kg ball from an elevated
tee, giving the ball an initial horizontal speed of 40
m/s (about 90 mi/hr). What is the magnitude of the
average force exerted by the club on the ball
during this time?
6.2 Impulse
In some cases, contact time may be shortened
to maximize the impulse. However, the contact
time can also be manipulated to reduce the
amount of force.
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6.2 Impulse
• A 70 kg worker jumps stiff-legged from a
height of 1.00 m onto a concrete floor.
– A.) What is the magnitude of the impulse he
feels on landing, assuming a sudden stop in
8.00 ms?
– B.) What is the average force?
6.2 Impulse
• Collisions? How do you define a collision?
• Does there have to be some type of contact
force for a collision?
• Collisions range from subatomic particles to
automobiles in traffic accidents.
6.2 Impulse
• Kinetic Energy and Momentum are very
closely related (they are different
quantities…but still they like each other!)
• K = p2
2m
6.3 Conservation of Linear
Momentum
If there is no net force acting on a system, its
total momentum cannot change.
Forces must be balanced, which means
FNET is equal to ????
This is the law of conservation of momentum.
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6.3 Conservation of Linear
Momentum
In this example, there is no external force, but
the individual components of the system do
change their momenta:
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6.3 Conservation of Linear
Momentum
Collisions happen quickly enough that any
external forces can be ignored during the
collision. Therefore, momentum is conserved
during a collision.
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6.4 Elastic and Inelastic Collisions
In an elastic
collision, the total
kinetic energy is
conserved.
Total kinetic energy
is not conserved in
an inelastic
collision.
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6.4 Elastic and Inelastic Collisions
A completely inelastic
collision is one where the
objects stick together
afterwards.
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6.4 Elastic and Inelastic Collisions
The fraction of the total kinetic energy that is
left after a completely inelastic collision can
be shown to be:
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6.4 Elastic and Inelastic Collisions
For an elastic collision, both the kinetic
energy and the momentum are conserved:
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6.4 Elastic and Inelastic Collisions
Collisions may take
place with the two
objects approaching
each other, or with
one overtaking the
other.
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6.5 Center of Mass
Definition of the center of mass:
The center of mass is the point at which all of the
mass of an object or system may be considered to be
concentrated, for the purposes of linear or
translational motion only.
We can then use Newton’s second law for the
motion of the center of mass:
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6.5 Center of Mass
The momentum of the center of mass does
not change if there are no external forces on
the system.
The location of the center of mass can be
found:
This calculation is straightforward for a
system of point particles, but for an
extended object calculus is necessary.
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6.5 Center of Mass
The center of mass of a flat object can be
found by suspension.
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6.5 Center of Mass
The center of mass may be located outside a
solid object.
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6.6 Jet Propulsion and Rockets
If you blow up a balloon and then let it go,
it zigzags away from you as the air shoots
out. This is an example of jet propulsion.
The escaping air exerts a force on the
balloon that pushes the balloon in the
opposite direction.
Jet propulsion is another example of
conservation of momentum.
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6.6 Jet Propulsion and Rockets
This same phenomenon explains the
recoil of a gun:
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6.6 Jet Propulsion and Rockets
The thrust of a rocket works
the same way.
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6.6 Jet Propulsion and Rockets
Jet propulsion can be used to slow a rocket
down as well as to speed it up; this involves
the use of thrust reversers. This is done by
commercial jetliners.
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Summary of Chapter 6
Momentum of a point particle is defined as
its mass multiplied by its velocity.
The momentum of a system of particles is
the vector sum of the momenta of its
components.
Newton’s second law:
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Summary of Chapter 6
Impulse–momentum theorem:
In the absence of external forces,
momentum is conserved.
Momentum is conserved during a collision.
Kinetic energy is also conserved in an
elastic collision.
© 2010 Pearson Education, Inc.
Summary of Chapter 6
The center of mass of an object is the point
where all the mass may be considered to be
concentrated.
Coordinates of the center of mass:
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