(Linear) Momentum (p)
● Momentum is mass times velocity
p = mv
momentum is a vector!
momentum has units kg*m/s
Which has more momentum?
Both have the
 1 kg object moving at 1000 m/s -or- same momentum!
a 1000 kg object moving at 1 m/s
 a rolling marble –or-
(p = 1000 kg*m/s)
The rolling marble has more momentum!
A truck has no momentum because it isn’t
stationary truck.
moving.
The truck has more
 a marble moving at 0.5 m/s –or- momentum. If two objects
are moving at the same
truck moving at 0.5 m/s
speed, the heavier one has
more momentum.
The way we use the word ‘momentum’ in
everyday life actually does relate to its
physics definition.
For example, in game, a sports announcer might say that
one team ‘has momentum’. What do they mean?
The sports announcer means that the team is really on the
move and is going to be hard to stop.
In this way, the everyday usage and the physics
definition of momentum are the same:
Any object with momentum is going to be hard to
stop or change.
How do we change momentum?
Since mass doesn’t (usually) change, a change in momentum
occurs when the velocity of an object changes.
Dp = mvf - mvi
What is necessary to change an object’s velocity?
Force!
Changes in momentum are produced by the action of
forces over time. Force applied over time (F∆t) is
called an impulse.
F∆t = ∆p
units: Ns = kg m/s
Impulse & momentum
∆p = F∆t
 Two cars are moving with the same velocity.
– In car A, the driver applies the brakes, and the car
stops due to the force of friction. The time period over
which friction acts is 30 seconds.
– Car B hits a tree. The time period over which the tree
applies a force is 0.5 seconds.
How does the change in momentum of the two objects
compare?
How does the force applied in each circumstance
compare?
Other examples of minimizing
force applied by maximizing time
of contact
Can you think of any examples?
 Air bags
 Safety nets used by acrobats
 Bending your knees when jumping from heights
 Moving with a punch
 Wearing boxing gloves
Other examples
 techniques in karate:
increase force by
increasing change of
momentum
 Following through
when hitting a ball:
This increases change
in momentum by
increasing the time
the force is applied.
We do
∆ p = F ∆t
∆p/F=∆t
(mvf – mvi) / F = ∆ t
(0.3*80 – 0.3*-60)/350 = 0.12 sec
We do
You Do
1) A compact car with mass 725 kg is moving 115 km/hr to the
East. The driver suddenly applies the brakes hard for 2.0s,
applying an average force of 5.0 X 103 N on the car.
a) What is the change in momentum of the car?
b) What is the final velocity of the car?
2. In a ballistics test at the police department, Officer Rios fires a
6.0 g bullet at 350 m/s into a container that stops it in 0.0018
s. What is the average force that stops the bullet?
You Do
1) A compact car with mass 725 kg is moving 115 km/hr to the
East. The driver suddenly applies the brakes hard for 2.0s,
applying an average force of 5.0 X 103 N on the car.
a) What is the change in momentum of the car? 10,000 Ns
b) What is the final velocity of the car? 18 m/s OR 65 km / hr
2. In a ballistics test at the police department, Officer Rios fires a
6.0 g bullet at 350 m/s into a container that stops it in 0.0018
s. What is the average force that stops the bullet? 1100 N
Graphical determination of momentum
In the problems we’ve done so far, the we’ve dealt with average
or constant force. If force changes over time, we can find the
change in momentum graphically.
Change in momentum, Δp, is the area under the
graph force vs. time.
The graph shows the force applied to
a 57 g tennis ball by a racquet over
time.
a) What is the change in
momentum?
∆p = area = 1/2b*h = ½* 0.3*6
∆p = 0.9 Ns
b) If the ball starts at rest, what is
its final velocity?
∆p = mvf
0.9 / 0.057 = 16 m/s
You do: Graphical determination of ∆p
a) What is the change
in momentum of the
football as a result
of being kicked?
b) If the football
started at rest, what
is its final velocity?
(mass = 400 g)
You do: Graphical determination of ∆p
a) What is the change
in momentum of the
football as a result
of being kicked?
∆p ≈ 9 Ns
b) If the football
started at rest, what
is its final velocity?
(mass = 400 g)
v ≈ 23 m/s