Objective:

At the end of the lesson, you

will be able to explain how
Galileo inferred that objects in
vacuum fall with uniform
acceleration.
The viewpoint of Aristotle regarding
freely falling objects which
prevailed until the 17th century was
challenged by Galileo. Galileo
disproved Aristotle’s theory by
pure reasoning and logical
arguments.
 Galileo’s experiment using three boxes of equal
weights

Figure 1. When the three boxes are placed side to

side and made to fall from the same height at the
same time, they will fall to the bottom at the same
time. If box A was glued to box B and made to fall at
the same time as box C, they will still reach the
bottom at the same time.
Imagine yourself holding a bowling
ball and a ping pong ball. If you
drop these balls simultaneously,
which ball do you think would have
greater acceleration upon reaching
the ground? Why?
Galileo proved with his experiments that when
objects are dropped simultaneously, they will reach
the ground at the same time regardless of their
masses and air resistance. In another set of
experiments, he discovered that objects fall with
uniform acceleration.
Galileo was fascinated by the behavior of falling
objects. He knew that falling objects increase their
speed as they go down. This change in speed is
acceleration. However, he did not have any
equipment to measure this change, so he used
inclined planes to lessen the acceleration of the
moving bodies. He was then able to investigate the
moving bodies carefully.
On his experiment, he had observed the
following:
 A ball rolling down an inclined plane
increases its speed by the same value after
every second. For example, the speed of a
rolling ball was found to increase by 2 m/s
every second. This means that the rolling
ball would have the following speeds for
every given second.
On his experiment, he had observed the
following:
 As the inclined plane becomes steeper,
the acceleration of the rolling ball
increases.
 The maximum acceleration of the rolling
ball was reached when the inclined plane
was positioned vertically as if the ball is
simply falling.
Example
Hold a book and a piece of paper at the
same height, then drop them
simultaneously. Did the objects reach the
ground at the same time? If no, which
object reached the ground first?
Now, perform the same procedure, but this
time, crumple the paper. Did the objects
reach the ground at the same time? If no,
which object reached the ground first?
This experiment agrees with Galileo’s
findings that when there is little or no air
resistance, objects that are dropped
simultaneously will reach the ground at the
same time, regardless of their masses.
Given that both objects (paper and book)
reached the ground simultaneously, we
can infer that the increase in speed of each
object is equal. Therefore, falling objects
have the same acceleration when there is
no air resistance (e.g. vacuum).
Key Points
 A body with uniform acceleration
changes its speed by a constant value.
 Galileo proved that when objects are
released simultaneously from a certain
height, they reach the ground at the
same time, regardless of their masses
and air resistance.
 Galileo discovered that all objects fall
with the uniform acceleration in
vacuum.
For many centuries, nobody was successful in
challenging Aristotle’s ideas. After two
thousand years, Galileo was able to challenge
Aristotle’s theories about motion. He tested
Aristotle’s ideas through “thought” experiments
which he did not actually perform except in his
mind. However, he arrived at conclusions
through logical thought. Through his
experiments, and with a clear logic and
mathematical knowledge, he showed that a body
moving along a frictionless horizontal surface
does not need an external force to maintain its
uniform speed.
Galileo tested his assertions by letting balls run
down bent rails. As the ball is released from
position A and allowed to run down the bent rail
ABC, the ball rises to position C, which is nearly
the same height as A. The ball is also made to
run down the bent rail ABD and ABE and the
ball again rises to nearly the same height as
position A. He observed that as the ball rolls
down the rail, its speed increases; as it rolls up,
its speed decreases. Consequently, the ball will
only reach nearly the same height as the original
position. This difference in height is due to the
friction between the ball and the rail surface.
He also observed that as the ball runs down the
bent rail, its speed increases. However, as the
ball moves up the rail, its speed decreases. This
change in speed is due to gravity.
When the ball is made to run down the bent rail
ABF, where BF is horizontal, the ball will never
be able to rise to nearly the same height as
position A. Instead, the ball will continue to move
at constant speed in a straight line.
Figure 2. When the ball rolls down the bent rail
AB, it increases its speed because it is moving
with gravity. When the ball rolls up the bent rail
BC, it moves against gravity, decreasing its
speed.
Galileo showed that there is a natural tendency for
objects to continue its state of motion unless a push or
a pull compels it to change that state. If the ball is
moving, it will continue to do so at constant velocity
just as it will remain at rest if it was stationary. Galileo
called this natural tendency inertia.

His assertions became the inspiration for Newton’s first

law of motion. They both imply that no force is needed
to keep the motion of an object and that the object’s
inertia would keep it from changing its state of motion.
Newton’s first law of motion states that “an object at
rest remains at rest and an object in motion remains in
motion at constant speed and constant direction unless
acted upon by an external force.”
There is a very subtle difference between
Galileo’s assertion and Newton’s first law
of motion. The difference lies in the
concept of force. Galileo knew about
friction but did not know about the concept
of force. He used the terms “push and pull”
to signify forces.
It was Sir Isaac Newton who defined the
concept of force and its relation to motion.
Newton’s first law of motion is also called
the Law of Inertia.
The motion of a ball falling from the sky or
a model rocket being launched up into the
atmosphere are examples of the law of
inertia.
It can also be used to explain the principle
behind safety features used in cars such as
seat belts, head rest and air bags. These
safety features are installed to prevent
injuries to passengers.
If a speeding car suddenly stops, the driver
and the passenger are thrown forward. This is
due to inertia keeping them moving forward.
On the other hand, when a car accelerates, the
driver and the passenger tend to move
backward because of their tendency to remain
at rest. This could also happen during
collision where the passenger is thrusted
forward while the head tends to remain at rest.
This could lead to serious head injuries which
can be life threating. This is the reason why
cars are now equipped with these safety
features.
Seat belts and air bags are designed to protect the
passengers from injuries if they are thrown forward
while head rests are designed to protect passengers if
they are thrown backward. The law requires that the
driver and passengers wear seatbelts.