The sports announcer says "Going into the
all-star break, the Chicago White Sox have the
momentum." The headlines declare "Chicago Bulls
Gaining Momentum." The coach pumps up his
team at half-time, saying "You have the momentum;
the critical need is that you use that momentum
and bury them in this third quarter."

Momentum is a
commonly used term in sports. A team that has the momentum
is on the move and is going to take some effort to
stop. A team that has a lot of momentum is really on the
move and is going to be hard to stop. Momentum is
a physics term; it refers to the quantity of motion that an
object has. A sports team which is on the move has
the momentum. If an object is in motion (on the move)
then it has momentum.

Momentum
can be defined as "mass in motion." All objects have mass;
so if an object is moving, then it has momentum - it has its
mass in motion. The amount of momentum which an object has
is dependent upon two variables: how much stuff is
moving and how fast the stuff is moving. Momentum
depends upon the variables mass
and velocity.
In terms of an equation, the momentum of an object is equal
to the mass of the object times the velocity of the
object.

Momentum = mass •
velocity

In physics, the symbol for the quantity
momentum is the lower case "p". Thus, the above equation can
be rewritten as

p = m •
v

where m is the mass
and v is the velocity.
The equation illustrates that momentum is directly
proportional to an object's mass and directly proportional
to the object's velocity.

The units for momentum would be mass units
times velocity units. The standard metric unit of momentum
is the kg•m/s. While the kg•m/s is the standard
metric unit of momentum, there are a variety of other units
which are acceptable (though not conventional) units of
momentum. Examples include kg•mi/hr, kg•km/hr, and
g•cm/s. In each of these examples, a mass unit is
multiplied by a velocity unit to provide a momentum unit.
This is consistent with the equation for momentum.

Momentum is a
vector quantity. As
discussed in an earlier unit, a
vector quantity is a quantity which is fully described
by both magnitude and direction. To fully describe the
momentum of a 5-kg bowling ball moving westward at 2 m/s,
you must
include information about both the magnitude and the
direction of the bowling ball. It is not enough to
say that the ball has 10 kg•m/s of momentum; the
momentum of the ball is not fully described until
information about its direction is given. The direction of
the momentum vector is the same as the direction of the
velocity of the ball. In a previous unit, it was said that
the direction of the velocity
vector is the same as the direction which an object is
moving. If the bowling ball is moving westward, then its
momentum can be fully described by saying that it is 10
kg•m/s, westward. As a vector quantity, the momentum of
an object is fully described by both magnitude and
direction.

From the definition of momentum, it
becomes obvious that an object has a large momentum if
either its mass or its velocity is large. Both variables are
of equal importance in determining the momentum of an
object. Consider a Mack truck and a roller skate moving down
the street at the same speed. The considerably greater mass
of the Mack truck gives it a considerably greater momentum.
Yet if the Mack truck were at rest, then the momentum of the
least massive roller skate would be the greatest. The
momentum of any object which is at rest is 0. Objects at
rest do not have momentum - they do not have any
"mass in motion." Both variables - mass
and velocity - are important in comparing the momentum of
two objects.

The momentum equation
can help us to think about how a change in one of the two
variables might affect the momentum of an object. Consider a
0.5-kg physics cart loaded with one 0.5-kg brick and moving
with a speed of 2.0 m/s. The total mass of loaded
cart is 1.0 kg and its momentum is 2.0 kg•m/s. If the
cart was instead loaded with three 0.5-kg bricks, then the
total mass of the loaded cart would be 2.0 kg and its
momentum would be 4.0 kg•m/s. A doubling of the mass
results in a doubling of the momentum.

Similarly,
if the 2.0-kg cart had a velocity of 8.0 m/s (instead of 2.0
m/s), then the cart would have a momentum of 16.0
kg•m/s (instead of 4.0 kg•m/s). A
quadrupling in velocity results in a
quadrupling of the momentum. These two examples
illustrate how the equation p = m•v serves as a "guide
to thinking" and not merely a "plug-and-chug
recipe for algebraic problem-solving."

Check
Your Understanding

Express your understanding of the concept and mathematics
of momentum by answering the following questions. Click the
button to view the answers.

1. Determine the momentum of a ...

a. 60-kg halfback moving eastward at 9 m/s.

b. 1000-kg car moving northward at 20 m/s.

c. 40-kg freshman moving southward at 2 m/s.

2. A car possesses 20 000 units of momentum. What would
be the car's new momentum if ...

a. its velocity were doubled.

b. its velocity were tripled.

c. its mass were doubled (by adding more passengers
and a greater load)

d. both its velocity were doubled and its mass were
doubled.

3. A halfback (m = 60 kg), a tight end (m = 90 kg), and a
lineman (m = 120 kg) are running down the football field.
Consider their ticker tape
patterns below.

Compare the velocities of these three players. How many
times greater is the velocity of the halfback and the
velocity of the tight end than the velocity of the
lineman?