1Newtonian dynamics of particles
IA Dynamics and Relativity
1.3 Newton’s Second Law
Newton’s second law is often written in the form of an equation.
Law. The equation of motion for a particle subject to a force F is
dp
dt
= F,
where
p
=
mv
=
m
˙
r
is the (linear) momentum of the particle. We say
m
is the
(inertial) mass of the particle, which is a measure of its reluctance to accelerate.
Usually, m is constant. Then
F = ma = m
¨
r.
Usually,
F
is specified as a function of
r,
˙
r
and
t
. Then we have a second-order
ordinary differential equation for r.
To determine the solution, we need to specify the initial values of
r
and
˙
r
, i.e.
the initial position and velocity. The trajectory of the particle is then uniquely
determined for all future (and past) times.