Mechanics 2: Linear and Rotational Dynamics - 3D Math Primer for Graphics and Game Development - page 555

This seems like quite a simple statement, even in the anachronistic trans-
lation of Newton's original Latin. But consider how audacious it was for
Newton to assert this, when it so clearly is at odds with the commonsense
observations we all have from our daily lives! A more “commonsense” way
to think about force is to assume that force is needed not only to start an
object in motion, but also to maintain its motion. (This is the rule under
so-called Aristotelian dynamics.) After all, once we stop applying the force,
eventually the object will stop moving, right? According to Newton, once
an object is set in motion, it does not require any force to continue this
motion. In fact, Newton claims that the force is required to stop the object,
and absent this stopping force, the object will continue on indefinitely.
Of course, the reason Newton's first law seems counterintuitive is that
in our everyday experience, when we set objects in motion, they are always
brought to a stop by the ubiquitous force of friction. But we can argue
that Newton's law is correct, even though objects always come to a stop
through friction, with a simple thought experiment. Imagine we apply a
certain amount of force and set an object in motion across a surface. The
object will travel a certain distance and eventually come to a stop. Did it
stop due the lack of continued pushing force, or due to some force that acted
to slow it down? If we perform the same experiment on different surfaces,
performing the initial push in the same manner in each case, we find that
the object travels farther on a smoother surface, and less distance on a
rougher surface. You probably aren't surprised at these ”commonsense”
results, but notice how they actually contradict the notion that a force is
required to keep the object in motion and validate Newton's laws.
Newton clarified the precise relationship among mass, acceleration, and
net force in his second law.

Newton's Second Law

The acceleration of a body is proportional to (and in the same direction
as) the net external force acting on the body, and inversely proportional to
the mass of the body:

f = m a . (12.1)

This simple equation is the most important one in this chapter. You
should certainly memorize it. It basically says that whenever a particle
with mass m is seen accelerating at a rate a , you can be sure that there
is a net force f acting on the particle. Likewise, whenever there is a net