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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