122
Summary
Selected Vocabulary
component........................the part of a velocity, acceleration, or force that would be perceptible to an
observer who could only see the universe projected along a certain one-
dimensional axis
parabola............................the mathematical curve whose graph has y proportional to x
2
Notation
x, y, z.................................an object’s positions along the x, y, and z axes
v
x
, v
y
, v
z....................................................
the x, y, and z components of an object’s velocity; the rates of change of
the object’s x, y, and z coordinates
a
x
, a
y
, a
z....................................................
the x, y, and z components of an object’s acceleration; the rates of change
of v
x
, v
y
, and v
z
Summary
A force does not produce any effect on the motion of an object in a perpendicular direction. The most
important application of this principle is that the horizontal motion of a projectile has zero acceleration, while
the vertical motion has an acceleration equal to g. That is, an object’s horizontal and vertical motions are
independent. The arc of a projectile is a parabola.
Motion in three dimensions is measured using three coordinates, x, y, and z . Each of these coordinates
has its own corresponding velocity and acceleration. We say that the velocity and acceleration both have x, y,
and z components
Newton’s second law is readily extended to three dimensions by rewriting it as three equations predicting
the three components of the acceleration,
a
x
= F
x,total
/m ,
a
y
= F
y,total
/m ,
a
z
= F
z,total
/m ,
and likewise for the first and third laws.
Chapter 6Newton’s Laws in Three Dimensions