Transcript Newton`s laws, forces

PH 201
Dr. Cecilia Vogel
Lecture
REVIEW
Projectiles
Dropping
Upward throw
Range
OUTLINE
Newtons Laws
Force, mass, inertia
action, reaction forces
Special Case: Uniform Circular
Motion

Direction angle changes at a constant rate
  wt
w is the (constant) “angular velocity”
positive if CCW
So x and y change sinusoidally
x-axis
Period of Motion
Period, T, is the time it takes
time to go
If it goes all the way
around once, the angle
changes by (rad)
If it goes all the way
around once, the distance
traveled is
  2
2
T
| w | v | w | r
d  2 r
2 r
v
T
Special Case:
Uniform Circular Motion
An object moves in a circle of constant
radius, r, with constant speed, v.
Is the object accelerating?

Consider ways of ID’ing acceleration:
physical intuition: force needed, jerk felt
math:
Acceleration
What is the acceleration of the object at
Consider the average acceleration from just
before to just after:
v i is
v f is
v is
so a is
Generally: centripetal
acceleration is
Magnitude of Acceleration
2
v
ac 
r
4 r
ac  2
T
Same r and larger v yields:

Same v and smaller r yields:

Same T and larger r yields:


2
Example
What is the speed and acceleration of the
Earth in orbit?
r = 93,000,000 mi = 1.5X1011 m
T = 1yr = 3.156X107s
= 30,000 m/s
= 0.0059 m/s2
huge circle –
Newton’s 1st Law
An object at rest remains at rest,
object in motion remains in uniform motion
(i.e. constant velocity, no change in
speed nor direction)
unless acted on by a net external force.
demos
Inertia
Inertia is the word used to describe this
tendency:
It is NOT a resistance to motion
It is a resistance to CHANGE in motion
Inertia is a property of matter.
Define mass: if an object has inertia, then
it has mass.
Centripetal Force – 1st Law
Recall: 1st Law
An object in motion will continue

no change
Can only continue
in circle if
Newton’s Second Law
An net external force can change an object's
velocity, can accelerate it.
The force required is proportional to the
acceleration, and in the same direction.
The force required is also proportional to
the object’s mass.
F  ma
Newton’s Second Law Improved
What is meant by “net” external force?
take all the external forces, and add them as
vectors.
the resultant is the net force.
Notation: S means sum
SF  ma
Note:
there may be several forces; add them.
there is only one acceleration.
Centripetal Force – 2nd Law
Recall: centripetal acceleration
An object moving in a circle
is accelerating
Recall: 2nd Law
in order for object to accelerate

SF  ma
The acceleration is toward center, so
centripetal force is
Centripetal Force – Examples
What force holds each in circular motion?
A ball swung around on a string:

You, as you rotate around with Earth’s
surface:

Amusement-park ride: you’re plastered to
the wall and the floor drops out

Coin on a turntable

Newton’s Third Law
“For every action, there is an equal and
opposite reaction”
Better said: “For every FORCE, there is
an equal and opposite reaction FORCE.”
If A pushes on B,
then B pushes back on A
at the same time.
Newton’s 3rd Law
For every FORCE, there is an equal and
opposite reaction FORCE.
If I try to push the door open, the door
pushes back on me,
making it hard to open a door in a
wheelchair.
If the Earth pulls down on me with
a gravitational force, then I pull up
on the Earth
with exactly the same size force!
More on the 3rd Law
The object pushes back, even if it
accelerates.
when you shoot a gun
you accelerate bullet forward
you can feel it push _________ on you
“recoil”
when you catch a ball
you accelerate it backward (to stop it)
you can feel it push __________ on you
3rd Law Reaction on What?
The “action” FORCE and the “reaction”
FORCE don’t act ON the same thing.
If the action force is Earth’s gravity pulling on ME,
then the reaction force is me pulling on the
Earth.
If the action force is your behind pushing down on
the chair,
then the reaction force is the chair pushing up
on your behind (keeping you from falling)