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Discussion Question
A. At the beginning of this section I represented the motion of a projectile on
graph paper, breaking its motion into equal time intervals. Suppose instead
that there is no force on the object at all. It obeys Newton’s first law and
continues without changing its state of motion. What would the corresponding
graph-paper diagram look like. If the time interval represented by each arrow
was 1 second, how would you relate the graph-paper diagram to the velocity
components v
x
and v
y
.
B. Make up several different coordinate systems oriented in different ways,
and describe the a
x
and a
y
of a falling object in each one.
6.3Newton’s Laws in Three Dimensions
It is now fairly straightforward to extend Newton’s laws to three dimen-
sions:
Newton’s First Law
If all three components of the total force on an object are zero, then it
will continue in the same state of motion.
Newton’s Second Law
An object’s acceleration components are predicted by the equations
a
x
= F
x,total
/m ,
a
y
= F
y,total
/m , and
a
z
= F
z,total
/m .
Newton’s Third Law
If two objects A and B interact via forces, then the components of their
forces on each other are equal and opposite:
F
A on B,x
= –F
B on A,x
,
F
A on B,y
= –F
B on A,y
, and
F
A on B,z
= –F
B on A,z
.
Chapter 6Newton’s Laws in Three Dimensions