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
is the (linear) momentum of the particle. We say
(inertial) mass of the particle, which is a measure of its reluctance to accelerate.
Usually, m is constant. Then
F = ma = m
is specified as a function of
. Then we have a second-order
ordinary differential equation for r.
To determine the solution, we need to specify the initial values of
the initial position and velocity. The trajectory of the particle is then uniquely
determined for all future (and past) times.