Newton

1
Newtons laws of motion

• Net force
• Action/reaction
• Inertial Reference frame
• Non-inertial Ref frame
• Mass
• Acceleration
• Friction
• Inertial Force
• Non-inertial Force
• Q Define as many of these concepts as you can?

2
First Law Law of Inertia
Q How does this animation relate to first
law? Q What is state of motion? Q Where is
unbalanced force applied ?
An object at rest (v0) remains at rest AND an
object at constant velocity (vc) remains at
constant velocity UNLESS acted upon by an
unbalanced force (Fnet not equal zero).
3
Second Law force definition
Acceleration is produced when a unbalanced force
acts on a mass. The greater the mass of the
object being accelerated the greater the amount
of force needed to accelerate the object.
4
Third law action/reaction
For every action, there is an equal and opposite
reaction. Force is always an interaction between
two objects that occurs and an action/reaction
force pair. No one object applies a force, both
apply equal and opposite force on each other. If
force was not always an action reaction pair,
momentum would NOT be conserved.
The rocket's action is to push down on the ground
with the force of its powerful engines, and the
reaction is that the ground pushes the rocket
upwards with an equal force.
5
Three Laws of classical mechanics

• In the absence of a net force, a body either is
  at rest or moves in a straight line with constant
  speed.
• 2. A body experiencing a force F experiences an
  acceleration a related to F by F ma, where m is
  the mass of the body. Alternatively, force is
  equal to the time derivative of momentum.
• 3. Whenever a first body exerts a force F on a
  second body, the second body exerts a force -F on
  the first body. F and -F are equal in magnitude
  and opposite in direction.

6
First Law Redux
Newton's first law is also called the law of
inertia. It states that if the vector sum of all
forces (that is, the net force) acting on an
object is zero, then the acceleration of the
object is zero and its velocity is constant.
The first point needs no comment, but the
second seems to violate everyday experience. For
example, a hockey puck sliding along ice does not
move forever rather, it slows and eventually
comes to a stop. According to Newton's first law,
the puck comes to a stop because of a net
external force applied in the direction opposite
to its motion. This net external force is due to
a frictional force between the puck and the ice,
as well as a frictional force between the puck
and the air. If the ice were frictionless and the
puck were traveling in a vacuum, the net external
force on the puck would be zero and it would
travel with constant velocity so long as its path
were unobstructed. Implicit in the discussion of
Newton's first law is the concept of an inertial
reference frame, which for the purposes of
Newtonian mechanics is defined to be a reference
frame in which Newton's first law holds true.
There is a class of frames of reference (called
inertial frames) relative to which the motion of
a particle not subject to forces is a straight
line. Newton placed the law of inertia first to
establish frames of reference for which the other
laws are applicable.To understand why the laws
are restricted to inertial frames, consider a
ball at rest inside an airplane on a runway. From
the perspective of an observer within the
airplane (that is, from the airplane's frame of
reference) the ball will appear to move backward
as the plane accelerates forward. This motion
appears to contradict Newton's second law (F
ma), since, from the point of view of the
passengers, there appears to be no force acting
on the ball that would cause it to move. However,
Newton's first law does not apply the stationary
ball does not remain stationary in the absence of
external force. Thus the reference frame of the
airplane is not inertial, and Newton's second law
does not hold in the form F ma.
7
Second law redux
Newton's second law states that the force applied
to a body produces a proportional acceleration
the relationship between the two is where F
is the force applied, m is the mass of the body,
and a is the body's acceleration. If the body is
subject to multiple forces at the same time, then
the acceleration is proportional to the vector
sum (that is, the net force) The second law
can also be shown to relate the net force and the
momentum p of the body Therefore, Newton's
second law also states that the net force is
equal to the time derivative of the body's
momentum
8
Second Law redux Impulse
An impulse I occurs when a force F acts over an
interval of time ?t, and it is given by Since
force is the time derivative of momentum, it
follows that This relation between impulse
and momentum is closer to Newton's wording of the
second law. Impulse is a concept frequently used
in the analysis of collisions and impacts.
9
The laws relationship to the conservation laws
In modern physics, the laws of conservation of
momentum, energy, and angular momentum are of
more general validity than Newton's laws, since
they apply to both light and matter, and to both
classical and non-classical physics. This can be
stated simply, "Momentum, energy and angular
momentum cannot be created or destroyed. Because
force is the time derivative of momentum, the
concept of force is redundant and subordinate to
the conservation of momentum, and is not used in
fundamental theories (e.g. quantum mechanics,
quantum electrodynamics, general relativity,
etc.).
10
Analysis of ball and feather fall in vacuum

• A vacuum is required to prove gravitational
  acceleration of an object is independent of its
  mass. The vacuum means that no air molecules are
  present to create friction on the falling object.
• This friction would resists the objects
  acceleration (greater velocity).
• Thus, any friction means that an object cannot be
  in a free-fall state.
• The vacuum is NOT why the feather and ball fall
  at same rate i.e., hit the bottom at same time
  with same velocity.
• The fact that gravity would be very constant over
  a few 10s of meters is also NOT why the masses
  fall at same rate.
• So, why does the feather and ball fall at same
  rate in a frictionless (airless) environment?

11
Why acceleration is independent of mass (without
friction)Larger Mass Larger gravity force
Larger Mass Larger inertial forceSo, Larger
gravity force is resisted by larger inertial
force This means acceleration is independent of
mass
12
Position, velocity and acceleration
1-D kinematic equations of motion
Projectile velocity along path
x position (m) v velocity (m/s) a acceleration
(m/s2) a ?v/ ?t (m/s/s m/s1/s m/s2 ) v
?x/ ?t (m/s m/s) What is relation between
x and t?
What is acceleration at vy 0 point?
13
acceleration
In physics, and more specifically kinematics,
acceleration is the change in velocity over
time.1 Because velocity is a vector, it can
change in two ways a change in magnitude and/or
a change in direction. In one dimension, i.e. a
line, acceleration is the rate at which something
speeds up or slows down. However, as a vector
quantity, acceleration is also the rate at which
direction changes.23 Acceleration has the
dimensions L T-2. In SI units, acceleration is
measured in metres per second squared (m/s2). In
common speech, the term acceleration commonly is
used for an increase in speed (the magnitude of
velocity) a decrease in speed is called
deceleration. In physics, a change in the
direction of velocity also is an acceleration
for rotary motion, the change in direction of
velocity results in centripetal (toward the
center) acceleration where as the rate of change
of speed is a tangential acceleration.
Acceleration is the rate of change of velocity.
At any point on a trajectory, the magnitude of
the acceleration is given by the rate of change
of velocity in both magnitude and direction at
that point. The true acceleration at time t is
found in the limit as time interval ?t ? 0.
14
Linear free-fall Zero to 30 m/s (60 mph) in 3
seconds!
15
Orbital free-fall

• If initial ball velocity this is slow (A,B) , the
  ball falls back to earth tracing out a parabolic
  path. Called ballistic trajectory.
• If initial ball velocity is too fast (E)
  (gtescape velocity) , the ball leaves earth
  traveling outward towards infinity and never
  comes back.
• Given correct initial ball velocity (C), the
  ball will go into orbit which means it is in
  continual free-fall as pull of gravity acts
  perpendicular to velocity vector to accelerate
  ball towards earth by the same amount that the
  earths surface curves away.
• Question what would happen if you were placed at
  1000 km above the earth and let go with no
  initial velocity ?

16
Centripetal acceleration
Why if string breaks does ball moves off in a
straight line?
17
Gravity field in Space shuttle
The gravity field strength diminishes as 1/r2
where r is reckoned with respect to center of the
earth. At earths surface 6400 km from center of
earth, the gravity field strength is 9.8
m/s2. So what is gravity field strength at 380
km above the earths surface which is the normal
height that the space shuttle orbits.
Orbital velocity at 380 km height is about 17,400
miles per hour (7800 m/s). The Orbital period
at 380 km height is about 92 minutes. Centripetal
acceleration for stable orbit must be a v2/r
78002 / 6.75e6 9.01 m/s2 . Does 8.74 9.01
m/s2 , it is close. I used approximate numbers
from the web. The gravity field is 88 of the
gravity at the surface. So, why are the people
weightless?
18
Weightlessness in orbit
Weightlessness in an orbiting spacecraft is
physically identical to free-fall, with the
difference that gravitational acceleration causes
a net change in the direction, rather than the
magnitude, of the spacecraft's velocity. This is
because the acceleration vector is perpendicular
to the velocity vector. In typical free-fall,
the acceleration of gravity acts along the
direction of an object's velocity, linearly
increasing its speed as it falls toward the
Earth, or slowing it down if it is moving away
from the Earth. In the case of an orbiting
spacecraft, which has a velocity vector largely
perpendicular to the force of gravity,
gravitational acceleration does not produce a net
change in the object's speed, but instead acts
centripetally, to constantly "turn" the
spacecraft's velocity as it moves around the
Earth. Because the acceleration vector turns
along with the velocity vector, they remain
perpendicular to each other. Without this change
in the direction of its velocity vector, the
spacecraft would move in a straight line, leaving
the Earth altogether.
19
Terminal velocity (falling through fluid)
In fluid dynamics an object is moving at its
terminal velocity if its speed is constant due to
the restraining force exerted by the air, water
or other fluid through which it is moving. A
free-falling object achieves its terminal
velocity when the downward force of gravity (Fg)
equals the upward force of drag (Fd). This causes
the net force on the object to be zero, resulting
in an acceleration of zero.1
When a falling object has reached terminal
velocity, is it still in free-fall state ?
20
Fields extend or propagate to infinite

• Gravity field from mass
• Electric field from charge
• Sound source wave field
• Electro-magnetic wave field

For r0, f(r) is undefined (infinite). For
limit as r ?8, f(r) 0. For all other r values
(domain), f(r) is finite.
Moral of story Fields never die. The
gravitational effects of you, me, the planet,
anything, extends to infinity! Although at far
distances, the effects becomes so small as to not
be measurable.