Physics 106 Lesson #4
Newton’s Laws of Motion
Dr. Andrew Tomasch
2405 Randall Lab
atomasch@umich.edu
Last Time: A Puzzle
• All objects near the earth are
attracted with the same
acceleration g = 9.8 m/s2 toward the
Earth’s center (“downward”)
irrespective of their masses
• Forces cause motion
• More massive objects have a
larger downward force acting on
them due to gravity
• How can these facts be
consistent?
• Enter Sir Isaac Newton!
The Three Laws
• First laid down by Isaac
Newton in his Principia
Mathematica in 1687
– Newton’s 1st Law: The Law of
Inertia
– Newton’s 2nd Law: Force and
Momentum (Acceleration)
– Newton’s 3rd Law: Action and
Reaction
• Built on the work of Galileo
• Considered the model of a
scientific treatise
Newton
Newton’s First Law:
The Law of Inertia
• “Every body continues in its state of
rest, or of uniform motion in a straight
line, unless it is compelled to change
that state by outside forces impressed
upon it.”
• Inertia (a scalar) is also called mass (m),
which is measured in kilograms (SI)
Newton’s First Law:
More Ways to Say It
• It is the natural tendency of objects to
keep on doing what they're doing.
• Objects do not change their state of
motion unless a FORCE is applied.
• No net force →momentum is constant (or
zero)→ velocity is constant (or zero) →
acceleration is zero.
Demo: Pulling the tablecloth from under the dishes
Why Seat Belts?
There is no “force” that ejects
the passenger. Rather, the
passenger continues to move
with a constant velocity after the
car has stopped, until something
applies a force to stop him (ouch!)
Caution
Quiz
Ahead
http://www.physicsclassroom.com/mmedia/newtlaws/cci.html
• If a car abruptly stops and seat belts are not
being worn, the passengers continue to
move in a straight line with the same speed.
• Newton’s First Law → Inertia
Concept Test #1
Harry and Sally are arguing in a bakery.
Harry says that if he throws his jelly donut
at her with a greater speed it will have a
greater inertia. Sally argues that inertia
does not depend upon speed, but rather
upon mass. With whom do you agree?
A)Harry
B)Sally
Inertia is simply another
word for mass. The more
mass, the more inertia.
Newton’s Third Law:
Action and Reaction
• “To every action there is always
imposed an equal reaction; or,
the mutual action of two bodies
upon each other are always
equal and directed to contrary
parts.”
Caution
Quiz
Ahead
FN → H = - FH → N
F12  F21
• Two rules:
– Third law pairs never act on the
same object.
– When one member of the action reaction pair is removed, the other
member also vanishes.
FH → N
Concept Test #2
You use your car to push a friend’s pickup
truck that has broken down. To bring both
of you to a stop, your friend applies the
brakes in the truck. In magnitude, the force
of the car on the truck is _______ the force
of the truck on the car.
A) greater than
B) equal to
C) less than The car exerts a force on the truck
(action). The truck exerts an equal
and opposite force on the car (reaction).
Newton’s Second Law
“The change in the
quantity of motion is
proportional to the
motive force impressed
and is made in the
direction of the line in
which that force is
impressed.”
Newton
Newton’s Second Law
and Momentum
In modern language, Newton’s
“quantity of motion” is called
momentum. Momentum is a
vector and is defined as the
product of an object’s mass and
velocity:
p  mv
Newton’s Second Law:
Momentum and Force
In it’s most general form,
Newton’s Second Law states
that the net external force acting
on an object equals the rate at
which its momentum changes
with time:
p
F
t
This is a
vector
equation
Newton’s Second Law:
Impulse and Momentum
If we multiply both sides of
Newton’s Second Law by time, we
get another way to say it: “The
impulse (force x time) delivered by
the net force equals the change in
an object’s momentum”
This is our jet
This is a
vector
equation
J  F t  p
This is also called the Impulse -- Momentum Theorem
car experiment
Force X Time =
Change in Momentum
Newton’s Second Law:
Force and Acceleration
Many objects do not change their mass
during motion. For these situations the mass
factors out of the momentum and we can
write Newton’s Second Law to relate force,
mass and acceleration:
p mvf  mvi m(vf  vi )
v
F


m
 ma
t
t
t
t
The direction of the force is
the same as the direction of
the acceleration
F  ma
This is a
vector
equation
Galileo’s Puzzle Solved!
F  ma
F  mg  ma
A Falling Object…
m
F  mg
a g
ag !
• All objects fall with the same
downward acceleration g !
• Same m on both sides →
Einstein’s Equivalence Principle
→ General Relativity
Our Hero!
+y
Rocket Science: Thrust
FThrust
vexhaust
Newton's Second Law :
P
t
Newton's Third Law :
F
Demo: Water Rocket
Ejected Momentum/Time Backward (Action)
Equals Thrust Force on Rocket Forward (Reaction) :
FThrust
 P 
  
  vex
 t  exhaust
 m 
 t  yˆ
ex
Thrust = Exhaust Speed x (Ejected Mass/Time)
Cannot be described with F = ma !
Newton’s Powerful Laws
• Account for most motions
• Newton’s laws don’t work:
– on atomic distance scales
(Quantum Mechanics)
– at speeds near the speed of light
(Einstein’s Special Theory of Relativity)
– in very strong gravitational fields (near
black holes
→ Einstein’s General Theory of Relativity)
• Newton’s laws apply to almost all
everyday situations
Newton
Newton’s Laws: Summary
• First Law: Objects continue their state of
motion (rest or constant velocity) unless acted
upon by a net external force.
• Second Law: The action of a net external force
on an object is to cause its momentum to
change with time. For objects with a constant
mass this can be written as F = ma.
• Third Law: Any object which exerts a force on
another object experiences an equal and
opposite force from the object it acts upon.