1
CHAPTER 8
IMPULSIVE FORCES
1.
Introduction.
As it goes about its business, a particle may experience many different sorts of forces.
In
Chapter 7, we looked at the effect of forces that depend only on the
speed
of the particle.
In a
later chapter we shall look at forces that depend only on the
position
of the particle.
(Such forces
will be called
conservative
forces.)
In this chapter we shall look at the effect of forces that vary
with
time
.
Of course, it is quite possible that an unfortunate particle may be buffeted by forces
that depend on its speed, on its position, and on the time - but, as far as this chapter is concerned,
we shall be looking at forces that depend only on the time.
Everyone knows that Newton's second law of motion states that when a force acts on a body, the
momentum of the body changes, and the rate of change of momentum is equal to the applied
force.
That is,
F
=
dp/dt
.
If a force that varies with time,
F
(
t
), acts on a body for a time
T
, the
integral of the force over the time,
∫
T
dt
t
F
0
,
)
(
is called the
impulse
of the force, and it results in a
change of momentum
∆
p
which is equal to the impulse.
I shall use the symbol
J
to represent
impulse, or the time integral of a force.
Its SI units would be N s, and its dimensions MLT
-1
,
which is the same as the dimensions of momentum.
Thus, Newton's second law of motion is
.
p
F
&
=
8.1.1
When integrated over time, this becomes
J
p
= ∆
.
8.1.2
Likewise, in rotational motion, the
angular momentum L
of a body changes when a
torque
τ
acts
on it, such that the rate of change of angular momentum is equal to the applied torque:
.
L
&
=
τ
8.1.3
If the torque, which may vary with time, acts over a time
T
, the integral of the torque over the
time,
∫
τ
T
dt
0
, is the
angular impulse
, which I shall denote by the symbol
K
, and it results in a
change of the angular momentum:
K
L
= ∆
.
8.1.4
The SI units of angular impulse are N m s, and the dimensions are ML
2
T
-1
, which are the same as
those of angular momentum.