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units of momentum should be:
m v = f ∆t,
M(L/T) = (ML/T 2 )T,
ML/T = ML/T.
Note that momentum is a vector quantity, having both magnitude and
direction.
To understand what momentum is, let's look at the two sides of Equa-
tion (12.16). First consider the left side, which interprets momentum as a
product of mass and velocity. In fact, somewhere in almost every physics
textbook you can find Equation (12.17).
Momentum as Product of Mass and Velocity
P = m v .
(12.17)
The variable P is the traditional variable used to represent momentum.
(Despite the capital letter, P is a vector quantity. We use capital P to
avoid confusion with the notation p , which we sometimes use to refer to
the position of a particle.)
Equation (12.17) makes it clear that the momentum of an object is an
instantaneous property of an object. By saying this, we mean that we
can define its value knowing only its instantaneous state, without worrying
about how it got into that state. Furthermore, if you think of momentum
as the “total amount of pushing” required to stop a moving object, then
it certainly is intuitively appealing that it should be the product of mass
and velocity. If the object is small and moving slowly (a pencil rolling on a
desktop), only a small total force will su ce. If it's fast (a bullet) or heavy
(a car that somebody left parked on an incline without the emergency brake
set), a larger amount will be needed. If it's fast and heavy (an airplane
coming in for a landing), then you'd better get out of the way. The equation
P = m v quantifies the idea of “hard to stop.”
Although the memorable equation P = m v from the left-hand side of
Equation (12.16) is perhaps the more common way of explaining momen-
tum, the right-hand side actually provides the most insight. The relation
P = f ∆t shows that momentum, as the product of force and time, is what
results when force acts over time. This is what was meant by the sloppy
phrase “total amount of pushing.” We don't mean that the magnitude of
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