Download Uniform Circular Motion

Uniform Circular Motion
Uniform Circular Motion
How does a roller coaster do a
loop without falling off the
track?
How is water removed from a
clothes washer?
Uniform Circular Motion
Does the velocity of an object
change when it is moving in a
circle?
Is the object accelerating
when it is moving in a
circle?
Uniform Circular Motion
Vtangential
velocity
Aacceleration
What is the
direction?
Uniform Circular Motion
v=v2-v1
a = v/t
Uniform Circular Motion
Centripetal acceleration (ac )
“Centerseeking”
acceleration
Dynamics of Uniform Circular
Motion
What force causes an object to
have centripetal acceleration?
Centripetal force - net force
necessary to cause centripetal
acceleration.
Dynamics of Uniform
Circular Motion
Centripetal force is
directed toward the
center of the circle.
Centripetal vs. Centrifugal Force
If centripetal means “center
seeking”, what does
centrifugal mean?
Does centrifugal force really
exist?
Centripetal vs. Centrifugal Force
If there was a
centrifugal
force, what
direction would
the ball travel
when the string
broke?
If there was a
centrifugal
force, the ball
would fly
outward
Uniform Circular Motion Lab
Uniform Circular Motion
Frames of Reference Video
Uniform Circular Motion
How does a roller coaster do a
loop without falling off the
track?
How is water removed from a
clothes washer?
Think about it!
What agent exerts the
centripetal force that keeps a
roller coaster from going in a
straight line?
What is the force called?
Think about it!
What agent exerts the
centripetal force that keeps a
the clothes from going outside
the washer bucket?
What is the force called?
Think about it!
What agent exerts the
centripetal force that keeps a
car going around a bend in the
road?
What is the force called?
Free body diagram of a car
going around a curve
Think about it!
What agent exerts the
centripetal force on the moon?
What is the force called?
Does the earth do work on the
moon? Explain.
Uniform Circular Motion
Centripetal acceleration
v

a r
C
2
Practice Problems 1-3
Practice Problems 3-5
v

m
F
r
2
c
Circumference = 2 π r
Think about it!
Which pulls harder, the earth
on the moon, or the moon on
the earth?
Newton’s Law of Universal
Gravitation
Newton
wondered
“Why does
an apple fall
and the
moon
doesn’t?”
Newton’s Law of Universal
Gravitation
Because the moon has
tangential velocity, so it
stays up.
But, the moon is held in
orbit by a centripetal force,
which he called “gravity”.
What do you know about gravity?
As the mass of an object
increases, the force of gravity
_______________.
Fg  mass
What do you know about gravity?
As the distance from the earth
decreases, the force of gravity
(Fg) _______________.
Fg  1/d
Newton’s Law of Universal
Gravitation
If Fg decreases as you increase
distance from the earth’s center,
how does g change?
Newton’s Law of Universal
Gravitation
Newton was able to calculate the
acceleration of the moon toward the
earth.
How?
He knew the orbital period (T) of the
2
moon
2
4 r
(
2

/
T
)

ac  r
2
T
Newton’s Law of Universal
Gravitation
Newton calculated that the
centripetal acceleration of the
moon toward the earth was
1/3600 the acceleration of an
object at the earth’s surface.
g/3600 = ac of the moon
Newton’s Law of Universal
Gravitation
Newton knew the moon was 60
earth radii away from the
center of the earth.
Since 602 = 3600…
Fc 1/distance2
Inverse square law
Centripetal Acceleration and
Gravity
Newton concluded that the
gravitational force of the
earth decreases as the
square of the distance from
the earth increases.
Newton’s Law of Universal
Gravitation
m1m2
FG  G 2
r
G = 6.67x10-11N-M2/kg2
Newton’s Law of Universal
Gravitation
The value of
G was
measured in
1798 by
Henry
Cavendish
Problems 6 and 7
Calculate the mass of the earth
Problem 8
Think About It! (True or False)
The force of Earth’s gravity
on the space shuttle in orbit
is zero or nearly zero.
“Weightlessness”
In free fall, an object undergoes
apparent weightlessness.
Measuring g
How could we measure the
acceleration due to gravity?
Pendulums are used to keep
time, measure g, and to show
that the earth spins on its axis.
Geophysical Applications
The value of g can vary on the
earth’s surface because of
(a)variations in elevation
(b) rock density.
Think About It!
How is the gravitational force
between two planets altered if the
mass of one planet doubles?
When the mass of both planets
doubles?
When they are three times as far
apart?
Planetary Motion
Copernicus – 1543
Proposed that the earth and
other planets orbit the sun in
perfect circles.
Planetary Motion
Brahe – 1570 Precise measurements of
planetary and stellar motion. Copernican
model did not explain the data
Planetary Motion
Kepler – 1595
Circular orbits don’t work but
elliptical orbits do!
Kepler’s Laws of Planetary
Motion
1. The paths of all planets are
ellipses with the sun at one
focus.
Kepler’s Laws of Planetary
Motion
Kepler’s Laws of Planetary
Motion
2. Each planet moves such
that an imaginary line drawn
from the sun to the planet
sweeps out equal areas in
equal time intervals. (Planets
move faster closer to the sun)
Kepler’s Laws of Planetary
Motion
Kepler’s Laws of Planetary
Motion
3. The square of a planet’s
orbital period (T2)
proportional to the cube of
the average distance
between the planet and the
sun (r3), or T2  r3
Kepler’s Laws of Planetary
Motion
Kepler’s third law can be used
to find orbital period and
orbital speed.
Rotational Motion
Center of mass – the
point at which all mass
of the body can be
considered to be
concentrated.
Rotational Motion
It’s the point at which an object
will rotate if only gravity is acting
on it.
Summary
Translational Rotational quantity
quantity
Inertia
Moment of inertia
Momentum
P=mv
Angular momentum
= moment of inertia x ang.
velocity
Torque
Torque = mass x ang. acceleration
Force
F=ma
Summary
Translational Rotational quantity
quantity
Inertia
Moment of inertia
Momentum
P=mv
Angular momentum
= moment of inertia x ang.
velocity
Torque
Torque = mass x ang. acceleration
Force
F=ma
Rotational Motion
Inertia – resistance to
translational motion; depends
on mass
Moment of inertia – resistance
to rotational motion; depends on
mass and distribution of mass
around the axis of rotation
Rotational Motion
As the farther the mass from the
axis of rotation the greater the
moment of inertia.
The greater the moment of inertia
the ______ it is to rotate the
object.
(flip pencil)
Conservation of Angular
Momentum
Gyroscope
video
Summary
Translational Rotational quantity
quantity
Inertia
Moment of inertia
Momentum
P=mv
Angular momentum
= moment of inertia x ang.
velocity
Torque
Torque = mass x ang. acceleration
Force
F=ma
Rotational Motion - Dynamics
Torque is the product of the force
times the length of the lever arm
Torque = force x lever arm
Unit : N-m
Rotational Motion - Dynamics
The greater the lever arm, the
______ the torque for the same
amount of force. The greater the
torque the ____ the angular
acceleration.
Summary
Translational Rotational quantity
quantity
Inertia
Moment of inertia
Momentum
P=mv
Angular momentum
= moment of inertia x ang.
velocity
Torque
Torque = mass x ang.
acceleration
Force
F=ma
Rotational Motion - Dynamics
Where can you apply the
least amount of force to open
or close a door?
Where can you hold a
baseball bat to get the
greatest acceleration of the
ball?
Numbered Heads Review
There is a gravitational force of
1.02 x 10-8N between a 75.0 kg
student and a 85.0 kg student.
How far apart are they?
Numbered Heads Review
Calculate the acceleration due
to gravity 15.6 km above the
surface of the earth.
Numbered Heads Review
By how many Newtons does
the weight of a 52 kg person
change when he goes from sea
level to an altitude of 12 km?
Numbered Heads Review
Mercury has a radius of 2.44
x 103 km and a mass of 3.30 x
23
10 kg. Calculate the
acceleration due to gravity on
the surface of Mercury in
2
m/s and g’s.
Numbered Heads Review
What is the force of gravity
acting on a 4500 kg spacecraft
when it is 3 Earth radii from
the Earth’s center?
Numbered Heads Review
A ball is whirled around on a
string that has a 0.55 m radius.
The ball takes 0.32 seconds to
make one revolution. What is
the centripetal acceleration of
the ball?