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down rapidly because there is no longer any force to make it continue in
motion. Once it is done with its forced motion, it changes to natural
motion, i.e. falling straight down. While the shot bullet is slowing down,
the dropped bullet gets on with the business of falling, so according to
Aristotle it will hit the ground first.
Luckily, nature isn’t as complicated as Aristotle thought! To convince
yourself that Aristotle’s ideas were wrong and needlessly complex, stand up
now and try this experiment. Take your keys out of your pocket, and begin
walking briskly forward. Without speeding up or slowing down, release
your keys and let them fall while you continue walking at the same pace.
You have found that your keys hit the ground right next to your feet.
Their horizontal motion never slowed down at all, and the whole time they
were dropping, they were right next to you. The horizontal motion and the
vertical motion happen at the same time, and they are independent of each
other. Your experiment proves that the horizontal motion is unaffected by
the vertical motion, but it’s also true that the vertical motion is not changed
in any way by the horizontal motion. The keys take exactly the same
amount of time to get to the ground as they would have if you simply
dropped them, and the same is true of the bullets: both bullets hit the
ground simultaneously.
These have been our first examples of motion in more than one dimen-
sion, and they illustrate the most important new idea that is required to
understand the three-dimensional generalization of Newtonian physics:
Forces have no perpendicular effects.
When a force acts on an object, it has no effect on the
part of the object's motion that is perpendicular to the
force.
In the examples above, the vertical force of gravity had no effect on the
horizontal motions of the objects. These were examples of projectile
motion, which interested people like Galileo because of its military applica-
tions. The principle is more general than that, however. For instance, if a
(horizontal scale reduced)
Aristotle
Newton
Chapter 6Newton’s Laws in Three Dimensions