Chapter 2 Motion
2-1. Speed
2-2. Vectors
2-3. Acceleration
2-4. Distance, Time, and
Acceleration
2-5. Free Fall System
2-6. Air Resistance
2-7. First Law of Motion
2-8. Mass
2-9. Second Law of Motion
2-10. Mass and Weight
2-11. Third Law of Motion
2-12. Circular Motion
2-13. Newton's Law of
Gravity
2-14. Artificial Satellites
2-1. Speed
• Definitions:
– Speed
• The rate at which something moves a given distance.
• Faster speeds = greater distances
– General formula for speed:
• Speed = distance / time
• Abbreviations commonly used:
d = distance t = time v = speed
v = d/t
2-1. Speed
Velocity
miles
 d   100miles 
v 
 40mph
  40
hour
 t   2.5hours 
Distance
 
d  v  t  30 miles

6
hours  180miles
hour
Time
miles
 d   100miles 
t  
 2.5hours
  2.5
miles / hour
 v   40miles / hour 
2-1. Speed
Average speed is the total
distance traveled by an
object divided by the
time taken to travel that
distance.
Instantaneous speed is
an object's speed at a
given instant of time.
2-2. Vectors
Magnitude of a quantity
tells how large the
quantity is.
Scalar quantities have
magnitude only.
Vector quantities have
both magnitude and
direction.
2-2. Vectors
Velocity is a vector quantity that includes both speed and
direction.
2-3. Acceleration
Acceleration of an object is the rate of change of its
velocity and is a vector quantity. For straight-line motion,
average acceleration is the rate of change of speed:
change in speed
Accelerati on 
time interval
vf  vi
a
t
2-3. Acceleration
3 Types of Acceleration
Speeding Up
Slowing Down
Turning
2- 4. Distance, Time and
Acceleration
Vavg =
(V1 + V2)
(20mph + 60mph)
2
2
= 40mph
d = vavg t
30mph 2hr = 60miles
d = ½at2
½ 10m/s/s 52 = 125m
2-5. Free Fall
The acceleration of
gravity (g) for objects
in free fall at the
earth's surface is 9.8
m/s2.
Galileo found that all
things fall at the same
rate.
2-5. Free Fall
The rate of falling
increases by 9.8 m/s
every second.
Height = ½ gt2
For example:
½ (9.8 )12 = 4.9 m
½(9.8)22 = 19.6 m
½ (9.8)32 = 44.1 m
½ (9.8)42 = 78.4 m
2-5. Free Fall
A ball thrown
horizontally
will fall at the
same rate as a
ball dropped
directly.
2-5. Free Fall
A ball thrown into the
air will slow down, stop,
and then begin to fall
with the acceleration
due to gravity. When it
passes the thrower, it
will be traveling at the
same rate at which it
was thrown.
2-5. Free Fall
An object thrown upward at an angle to
the ground follows a curved path called
a parabola.
2-6. Air Resistance
• In air…
– A stone falls faster
than a feather
• Air resistance
affects stone less
• In a vacuum
– A stone and a
feather will fall at
the same speed.
2-6. Air Resistance
• Free Fall
– A person in free
fall reaches a
terminal
velocity of
around 54 m/s
– With a
parachute,
terminal velocity
is only 6.3 m/s
• Allows a safe
landing
2-6. Air Resistance
• Ideal angle for a projectile
– In a vacuum, maximum distance is at an angle of 45o
– With air resistance (real world), angle is less
• Baseball will go furthest hit at an angle of around 40o
2-7. First Law of Motion
The first law of
motion states: If
no net force acts
on it, an object at
rest remains at
rest and an object
in motion remains
in motion at a
constant velocity.
Foucault Pendulum
Inertia keeps a pendulum
swinging in the same
direction regardless of the
motion of the earth. This
can be used to measure the
motion of the earth. As the
Foucault Pendulum swings
it appears to be rotating,
but it is the earth that is
rotating under it. To the
right is the Foucault
Pendulum at the Pantheon
in Paris, France.
Foucault Pendulum
Other Web sites that illustrate the Foucault Pendulum.
http://en.wikipedia.org/wiki/File:Foucaultrotz.gif
http://www.physclips.unsw.edu.au/jw/foucault_
pendulum.html
http://aspire.cosmicray.org/labs/scientific_method/pendulum.swf
http://www.calacademy.org/products/pendulum/
page7.htm
http://www.youtube.com/watch?v=nB2SXLYw
KkM
2-8. Mass
Inertia is the apparent resistance
an object offers to any change in
its state of rest or motion.
2-9. Second Law of Motion
Newton's second law
of motion states: The
net force on an object
equals the product of
the mass and the
acceleration of the
object. The direction of
the force is the same as
that of the acceleration.
F = Ma
2-9. Second Law of Motion
A force is any
influence that
can cause an
object to be
accelerated.
The pound (lb) is
the unit of force
in the British
system of
measurement:
1 lb = 4.45 N (1 N
= 0.225 lb)
1 newton  1 N  1 (kg)(m/s 2 )
2-10. Mass and Weight
• Weight
Definition: The force with which an object is
attracted by the earth’s gravitational pull
• Example: A person weighing 160 lbs is being pulled
towards the earth with a force of 160 lbs (712 N).
– Near the earth’s surface, weight and mass are
essentially the same
Weight  (mass)(acc eleration of gravity)
w  mg
2-11. Third Law of Motion
The third law of
motion states:
When one object
exerts a force on a
second object, the
second object exerts
an equal force in the
opposite direction
on the first object.
2-11. Third Law of Motion
Examples of the 3rd Law
2-12. Circular Motion
Centripetal force is the inward force exerted on an object
to keep it moving in a curved path.
Centrifugal force is the outward force exerted on the
object that makes it want to fly off into space.
2-12. Circular Motion
2-12. Circular Motion
833 N is needed to make this turn.
If he goes too fast, which wheels are likely to
come off the ground first?
2-13. Newton's Law of
Gravity
Gm1m2
Gravitatio nal force  F 
2
R
G = 6.67 x 10-11
N•m/kg2
2-13. Newton's Law of
Gravity
• How can we determine the
mass of the earth using an
apple?
– This illustrates the way
scientists can use indirect
methods to perform
seemingly “impossible
tasks”
2-13. Newton's Law of
Gravity
• How can we determine the mass of the
earth using an apple?
– This illustrates the way scientists can use
indirect methods to perform seemingly
“impossible tasks”
 GmM  = mg
Gravitational force on apple  F  

2
R


 gR 2  (9.8m / s 2 )(6.4 106 m) 2
24
M 


6

10
kg

11
2
2
 G  6.67 10 N  m / kg
2-15. Artificial Satellites
• The world's first artificial
satellite was Sputnik I, launched
in 1957 by the Soviet Union.
GPS-Global Positioning
Satellite
2-15. Artificial Satellites
The escape speed is the speed
required by an object to leave the
gravitational influence of an
astronomical body; for earth this
speed is about 40,000 km/h.
2-15. Artificial Satellites
The escape speed is the speed
required by an object to leave the
gravitational influence of an
astronomical body; for earth this
speed is about 40,000 km/h.
Rotation & Revolution
 Axis
 A straight line through which circular motion
takes place
 All points on object orbit around the axis
 All rotation/revolution requires an axis
Rotation & Revolution
 Rotation
 Object rotating about an internal axis
 Ex. Daily motion of the Earth, spiral football
 Revolution
 Object rotating about an external axis
 Ex. Yearly motion of the earth
How do we describe how fast
something is rotating??
 Speeds for objects in a straight line are
called linear (or tangential) speeds,
 Linear speeds are a rate at which an object
covers a certain distance (v =d/t)
 Ex. Unit – m/s , km/hr , mph
 Can’t express speeds of rotation with a
linear speed,
 b/c objects at different points on the rotating
object have different linear speeds
 Rotational speed
 Expresses the rate at which an object rotates
through a portion of a circle ( an angle)
 Ex. Unit --- RPM’s
Below, a record spinning on a axis through its
center (black dot)
 Faster linear speed, Star or Smiley??
Smiley, travels a greater distance for each
Full spin.
 Faster rotational speed, Star or smiley??
 Both the same, b/c entire record is rotating at the same rate
Are all people on Earth moving at the
same speed??
 Earth is rotating about an axis through its
poles
 So that means we are all moving since we
are all on the Earth.
 Are some of us moving with a greater
LINEAR SPEED than others??
 Yes, closer to the Equator, the faster you are
moving…. Closer to poles, the slower you are
moving
 Are some of us moving with a greater
ROTATIONAL SPEED than others??
 No, all people on earth have same rotational
speed, because Earth is spinning at the same
rate everywhere
Centripetal Acceleration
• Tangential speed (vt)
depends on distance
• When tangential speed
is constant, motion is
described as uniform
circular motion
• An object moving in a circle at a constant
speed still has an acceleration due to its
change in direction
• Velocity is a vector so acceleration can be
produced by a change in magnitude and
direction
• Centripetal Acceleration is acceleration
caused by a change in direction, directed
toward the center of a circular path
• ac = Vt2 / r
Centripetal Acceleration
Centripetal Force
 When driving in a circle, in what direction
?
is a force acting on you?
 Pushing you outward from the circle, or
inward?
 If you are swinging a yo-yo in a circle, and the
string breaks…. What path does the yo – yo
take??
 Ans. -- Inwards, toward the center of the
circle
 Ans -- yo- yo goes in a path tangent to
the circle
Centripetal Force
 HOWEVER, People commonly think
there is a force pushing you out from the
circle
 Feels like you are being pushed outward
 Example ….. The Rotor- amusement park
ride, a centrifuge, CD on your dashboard
moving to the right when your turning left
 Why is this??
The Rotor
People Stand with backs
against wall of a large cylinder,
cylinder then starts spinning,
and people are seemingly
pushed against the wall, then
floor drops, and people are
stuck against the wall.
http://www.youtube.com/watc
h?v=uz_DkRs92pM
So why is there no Force pushing you out
from the circle??
 A force does not cause this…… your
INERTIA does!!
 Inertia makes you want to stay in a
straight line, and by going in a circle,
you are fighting your own inertia
 This is how Rotor works, and why CD on
dashboard happens
 The only actual force acting on you is the
Centripetal Force
Centripetal Force
 Centripetal means “centerSeeking”
 Force pushes you toward the
center of the circle
 Is the force that keeps you
moving in a circle, and
keeps your inertia from
taking you in a straight line
Centripetal Force is affected
by.. Mass (m),
linear speed (vt),
and radius (r)
Centripetal Force
• Inertia wants to take objects in a tangent
line, to the circular path
• Inertia is why you feel like your being pushed
outward
– This outward pushing is sometimes called the
Centrifugal Force
• but it is not
actually a force, is only inertia
• Every object that moves in circular motion
must experience a centripetal force from
somewhere