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Chapter 6: Momentum
 12.1 Momentum
 12.2 Force is the Rate of Change of
Momentum
 12.3 Angular Momentum
Chapter 12 Objectives

Calculate the linear momentum of a moving object given the mass
and velocity.

Describe the relationship between linear momentum and force.

Solve a one-dimensional elastic collision problem using
momentum conservation.

Describe the properties of angular momentum in a system—for
instance, a bicycle.

Calculate the angular momentum of a rotating object with a
simple shape.
Chapter Vocabulary
 angular momentum
 collision
 law of conservation of
 momentum
 elastic collision
 gyroscope
 impulse
 inelastic collision
 linear momentum
 momentum
Inv 12.1 Momentum
Investigation Key Question:
What are some useful properties of
momentum?
12.1 Momentum
 Momentum is a property of moving matter.
 Momentum describes the tendency of objects
to keep going
 Net forces change momentum.
12.1 Momentum
 The momentum depends on mass and velocity.
 Ball B has more momentum than ball A.
12.1 Momentum
 If both ball A and B were pushed with the same force,
what can we determine about their difference?
12.1 Kinetic Energy and Momentum
 Kinetic energy and momentum are different, even
though both depend on mass and speed.
 Kinetic energy is a scalar quantity.
 Momentum is a vector, so it always depends on
direction.
12.1 Calculating Momentum
Momentum
(kg m/sec)
Mass (kg)
p=mv
Velocity (m/sec)
Comparing momentum
Calculate and compare the momentum of the
car and motorcycle.
1.
2.
3.
You are asked for momentum.
You are given masses and velocities.
Use: p = m v
4.
5.
Solve for car: p = (1,300 kg) (13.5 m/s) = 17,550 kg m/s
Solve for cycle: p = (350 kg) (30 m/s) = 10,500 kg m/s

The car has more momentum even though it is going much slower.
12.1 Conservation of Momentum
 The law of conservation of momentum states
that without an outside force, the total
momentum of the system is constant.
If you throw a rock forward from a
skateboard, you will move
backward in response.
12.1 Conservation of Momentum
12.1 Collisions in One Dimension
 A collision is when two or more objects hit
each other.
 During a collision, momentum is transferred
 Collisions can be elastic
or inelastic.
12.1 Collisions
Inelastic collisions
What is their combined velocity after the
collision?
1.
You are asked for the final velocity. You are given
masses, and initial velocity of moving train car.
3.
Diagram the problem, use m1v1 + m2v2 = (m1v1 +m2v2) v3
4.
Solve for v3= (8,000 kg)(10 m/s) + (2,000 kg)(0 m/s)
(8,000 + 2,000 kg)
v3= 8 m/s
The Archer
An archer at rest on frictionless ice fires a 0.5-kg arrow horizontally
at 50.0 m/s. The combined mass of the archer and bow is 60.0 kg.
With what velocity does the archer move across the ice after firing the
arrow?

pi  p f
m1v1i  m2 v2i  m1v1 f  m2v2 f
m1  60.0kg, m2  0.5kg, v1i  v2i  0, v2 f  50m / s, v1 f  ?
0  m1v1 f  m2 v2 f
m2
0.5kg
v1 f  
v2 f  
(50.0m / s)  0.417m / s
m1
60.0kg
May 22, 2017
12.1 Collisions in 2 and 3 Dimensions
 Most real-life collisions do not occur in one
dimension.
 In order to analyze two-dimensional collisions
you need to look at each dimension separately.
 Momentum is conserved separately in the x and
y directions.
12.1 Collisions in 2 and 3 Dimensions
12.2 Force is the Rate of Change of
Momentum
Investigation Key Question:
How are force and momentum
related?
12.2 Force is the Rate of Change of
Momentum
 Momentum changes when
a net force is applied.
 The inverse is also true:
 If momentum changes,
forces are created.
 If momentum changes
quickly, large forces are
involved.
12.2 Force and Momentum Change
The relationship between force and motion
follows directly from Newton's second law.
Force (N)
Change in time (sec)
F=Dp
Dt
Change in momentum
(kg m/sec)
Calculating force
Starting at rest, an 1,800 kg rocket takes off, ejecting
100 kg of fuel over a second at a speed of 2,500 m/sec.
Calculate the force on the rocket from the change in
momentum of the fuel.
1.
You are asked for force exerted on rocket.
2.
You are given rate of fuel ejection and speed of rocket
3.
Solve: Δ = (100 kg) (-2,500 m/s) = -250,000 kg m/s
4.
Use F = Δ ÷Δt
Solve: ΔF = (100 kg) (-250,000 kg m/s) ÷(1s)= - 25,000 N

The fuel exerts and equal and opposite force on rocket of +25,000 N.
12.2 Impulse
 Impulse measures a
change in momentum
because it is not always
possible to calculate force
and time individually
 Collisions happen so fast!
12.2 Force and Momentum Change
To find the impulse, you rearrange the
momentum form of the second law.
Impulse (N•sec)
FD t=Dp
Change in
momentum
(kg•m/sec)
Impulse can be expressed in kg•m/sec
(momentum units) or in N•sec.
Show from 5-6 min
12.2 Impulse
 What is the change of
momentum between these
two balls?
 Impulse = change in v * time
 aka change in momentum
12.2 Impulse
 What is the change of
momentum between these
two balls?
 Rubber ball change in
velocity is 4.
 Clay one the change is 2.
 So the rubber ball had
twice as much impulse
12.2 Impulse
 So things that bounce have a
great impulse, so they feel a
greater force!
12.2 Impulse
 You are given a choice at a carnival game of what
ball to throw at stacked milk jugs.
 Sandbag which stops when it hits
 A base ball which goes through
 And a rubber ball which bounces
12.2 Impulse
Which one do you choose?
 Sandbag which stops when it hits
 A base ball which goes through
 And a rubber ball which bounces
Take a vote
12.2 Impulse
 You choose the rubber ball because the
change in momentum is the most
 so the impulse is bigger.
 This means the force the ball feels is more.
 And with equal and opposite the
jugs feel more force too!
12.2 Impulse
 But which ball do they let you use in this
game?
12.2 Impulse
 This is why carnivals are evil