As it goes about its business, a particle may experience many different sorts of forces.
Chapter 7, we looked at the effect of forces that depend only on the
of the particle.
later chapter we shall look at forces that depend only on the
of the particle.
will be called
In this chapter we shall look at the effect of forces that vary
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
If a force that varies with time,
), acts on a body for a time
integral of the force over the time,
is called the
of the force, and it results in a
change of momentum
which is equal to the impulse.
I shall use the symbol
impulse, or the time integral of a force.
Its SI units would be N s, and its dimensions MLT
which is the same as the dimensions of momentum.
Thus, Newton's second law of motion is
When integrated over time, this becomes
Likewise, in rotational motion, the
angular momentum L
of a body changes when a
on it, such that the rate of change of angular momentum is equal to the applied torque:
If the torque, which may vary with time, acts over a time
, the integral of the torque over the
, is the
, which I shall denote by the symbol
, and it results in a
change of the angular momentum:
The SI units of angular impulse are N m s, and the dimensions are ML
, which are the same as
those of angular momentum.