120

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