P HYSICS NOTES
Introduction to Dynamics—Explaining Motion (II)
Galileo’s genius was in imagining cases where all sources of resistance to the motion were removed—perfectly
smooth ice and no air resistance, for instance. This of course is an imaginary situation, but it helps us to see the
essence of what’s happening. If a sled moves onto perfectly smooth ice, it will continue in its motion forever,
moving in a straight line with no loss of speed! Moreover, it will continue to move without anything
pushing it along!
The natural state of an object—its behavior if free from external influences—
is straight line motion with constant speed. We call this uniform motion.
In other words, when left alone, a moving object will continue to move in the
same direction with the same speed forever!
It’s not constant motion that needs to be explained. Rather, why objects don’t
continue in constant motion is what needs to be explained. Why does the sled,
in reality, come to rest? Why does an object’s motion change?
Galileo’s new viewpoint was that since the sled does, in reality, eventually come to a stop, there must be an
external influence causing it to depart from its natural state of uniform motion. Today we call such influences
that lead to deviations from uniform motion forces.
Force—An influence that leads to deviations from straight-line motion at constant speed.
A strong force has a different effect than a weak force. A force exerted in different directions has a different
effect. Since a force has a magnitude and a direction, force is a vector. Forces add together just like
any other vectors.
Net Force—The vector sum of all the forces acting on an object. Motion/rest depends on the net force.
Notice that “at rest” has no special significance in Galileo’s view of motion—it is simply uniform motion that
happens to have a velocity of zero. This means that an object at rest, in the absence of a net force, will
remain at rest forever! In a sense, this agrees with Aristotle’s perspective—an object at rest will naturally stay at
rest. But this is not because “at rest” is the state all objects naturally tend to, as Aristotle believed. Rather, the
correct perspective, Galileo’s perspective, is that the object remains at rest because there is not a net force present
to take it out of its state of uniform “motion” (which happens to have a velocity of zero).
Aristotle vs. Galileo
Aristotle
Galileo
Dynamics is determined by the nature of the element.
Different behavior for earth, water, air, fire.
All objects, substances, and elements are subject
to the same rules of nature.
An earthly object’s natural state is to be at rest.
The natural state of all objects is uniform motion.
Uniform motion requires a force.
Uniform motion does not require force.
An object in the absence of a force will come to rest,
its natural state.
A moving object in the absence of a net force will
move in a straight line with the same speed
forever. An object at rest will stay at rest.
An object at rest is in such a state by its own intrinsic
nature.
An object at rest is in such a state because there is
no net force to take it out of this state.
Motion must be explained.
Change in motion must be explained.
Galileo’s ideas were very much counter to those of Aristotle and his contemporaries in ancient Greece. While we
regard Galileo’s view as more accurate today, the depth of impact that Aristotle’s views had is exhibited in the
duration of his perspective—Aristotle’s ideas were not overturned for 2000 years!
Galileo’s experiments were limited to motion along horizontal surfaces. It was left to Isaac Newton (1643-1727)
to generalize Galileo’s above conclusions, and today we call this Newton’s First Law of Motion.
Working upon the foundation laid by Galileo, I propose my
first law of motion:
Consider an object with no net force acting on it.
If it is at rest, it will remain at rest.
If it is moving, it will continue to move in a straight line at
constant speed.
Conceptual Example. A crash test car collides head-on with a wall. As the front-end of the car collapses,
the car comes to a stop. However, the dummy in the car does not come to a stop, but instead continues
moving straight ahead. Only when the dummy violently hits the steering wheel/dash board does it stop.
Using Newton’s 1st law, explain the motion of (a) the car, and (b) the dummy.
Notice that Newton’s 1st law involves the net force acting on an object. If there is more than one force acting on an
object, we need to add as vectors all of these forces. The net force is the vector which results from adding up all of
the applied forces.
⃑ , than there is no net force acting on the
Notice that the net force is a single vector. If this vector is the zero vector, 0
st
object, and according to Newton’s 1 law, the object will remain in uniform motion if it is moving, or it will remain
at rest if it is at rest.
Question—You push your physics book across the top of your desk at a constant speed. You are exerting a force on
the book, and yet the book is moving with constant speed in a straight line. Why?
Fun Force Facts
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A force is a vector. It has both a magnitude and a direction.
A force can be thought of as a push or a pull on an object.
A force acts on an object—that thing to which the push or pull is applied.
A force requires an agent—something which does the pushing or pulling. The agent can be a hand,
foot, baseball bat, tabletop, wall, star, galaxy, etc.
A force is either a “contact” force or a long-range force. Pushing a door closed is an example of a
contact force. Gravity is an example of a long-range force—the sun pulls on the earth, though they
are not in contact.
Drawing Force Vectors
(1) Represent the object as a dot.
(2) Place the tail of the force vector on the dot.
(3) Draw the force vector as an arrow pointing in the proper direction
and with a length proportional to the size of the force.
(4) Give the vector an appropriate label.
𝐹
Step (2) may seem contrary to what a push does—shouldn’t we put the tip at the object? The answer is No.
Remember that it is the tail which says “this vector is acting at this position.”
Also note that we don’t include the agent in the drawing. We only show the force the agent is exerting.
𝐹
𝐹
𝐹
The pictures above show three examples of drawing force vectors. The first is a pull, the second a push, and the
third a long-range force, but in all three the tail of the force vector is placed on the dot representing the object.
Combining Forces
Below we have a top view of a box being pulled by two ropes. How will the box respond? Will it move, and if so, in
what direction? Experimentally, we find that when two or more forces are acting on an object, the forces combine
according to the rules of vector addition. The resultant force is known as the net force, as we have seen.
𝐹net = 𝐹1 + 𝐹2 + 𝐹3 + ⋯
It is very important to recognize that the net force 𝐹net is not a new vector acting in addition to the original
forces 𝐹1 , 𝐹2 , 𝐹3 , … . Instead, the original forces are replaced by 𝐹net .
In other words, 𝐹net is the single vector which, if it were acting on the object, would have precisely the same
result as all of the original force vectors acting on the object.
Example. Two of the three forces exerted on an object are shown. If the net force on the object is zero,
draw the missing force.
𝐹1
𝐹2