Last week, we discussed the kinematics of motion.
How one describes the motion of an object
by specifying its position, velocity, and acceleration
as a function of time.
This week, we will continue by discussing
the dynamics of motion.
How the application of forces on an object
changes the geometry or trajectory of its motion.
We will see that the applied forces and the change
in trajectory are related through Newton's laws
of motion.
We will begin by reviewing Newton's three laws of motion.
These were a landmark achievement
in scientific thought.
Most people who haven't studied physics
tend to intuitively think in terms of the ancient mechanics
of Aristotle in which an applied force is required to maintain
a body in uniform motion.
Superficially, this seems to agree
with our everyday experience, but only
because friction plays such an important role
in our everyday life.
One of Newton's great insights was
that applied forces cause changes in an object's motion,
rather than being necessary to maintain uniform motion.
Newton's laws were the end result
of a great deal of careful definition,
observation, and reasoning by many scientists
up to and including Newton.
It is a fascinating and compelling chapter
in the history of science, but we will not discuss
that history in this course.
Instead, we will simply state Newton's three laws of motion
as assumed postulates or axioms and discuss their meaning
and application.
Finally, we will consider several specific examples
of physical forces, such as gravity, contact forces exerted
by a solid surface, like the so-called normal force, which
acts perpendicular or normal to the surface,
and friction, which acts parallel to the surface,
pulling forces like tension in a rope or chain,
and the force exerted by a stretched or compressed spring
described by Hooke's law.
Taken as a whole, this week will show us
how to connect the two sides of Newton's Second Law of Motion,
f equals ma, the dynamics or application
of forces on the left-hand side and its relation
to the kinematics, the change in geometry of the object's motion
or trajectory, on the right-hand side.