Download Energy and Angular Momentum. Laws

Energy and
Angular
Momentum. Laws
of Conservation.
Announcements
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Homework # 2 is due on Friday, Oct. 7th.
First in-class exam will take place on Thursday,
October 6th.
¨  Please,
remember your STUDENT ID!!! (no ID no
Exam)
¨  Please remember to bring a pencil # 2.
¨  List of Textbook Units for Exam 1 are on the course
website (www.astro.umass.edu/~calzetti/astro100)
under the link `Exams’
¨  Homework # 2 offers good practice for the exam!
Assigned Reading
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Unit 20
Today s Goals
1) To introduce the concept of energy and
energy conservation.
2) To introduce the concept of angular
momentum, and angular momentum
conservation.
Energy and
Energy Conservation
What is Energy?
n  It
is the amount of total work an object (or
you) does or can do.
¨ You
need a good breakfast to store enough
energy for a good day of learning (work)
¨  If
we lift a rock from the ground, we `work against
gravity, and we store that `energy in the rock
(potential energy). That stored energy is released
when we let the rock go, and the rock falls to the
ground (kinetic [movement] energy); when the rock
impacts the ground, the kinetic energy is `dissipated
in thermal (heat) energy
Energy comes in different forms.
n  Kinetic
Energy
¨ Bulk
motion (the motion of a body)
¨ Thermal Energy (Heat)
n  Potential
Energy (will be explained soon!)
¨ Gravitational
potential energy
¨ Mechanical potential energy
¨ Electromagnetic potential energy
n  Radiative
¨ 
Energy
We ll spend at least one entire class on this one.
Energy is measured in Joules
n  A
Joule (J) is an amount of energy.
n  Power
is the rate of energy usage. Power
is measured in Watts (W) and is the
number of Joules used in one second.
1 W = 1 J/s (one horsepower = 745 W)
New energy is never created!
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All forms of energy on Earth and in the Universe
can be traced back to an earlier incarnation of
energy.
Why do sweet fruits
generally grow in the
south?
Energy can change form, but is never
created or destroyed!
Energy is conserved!
one form
of energy
Another form …
Kinetic Energy
n  Kinetic
energy is always due to some kind
of motion. Objects at rest have no kinetic
energy (KE=0).
You can calculate an objects kinetic energy
by knowing its mass and velocity.
KE = 1/2 mv2
mass
This is energy so it s measured
in Joules!
Velocity squared
KE = 1/2 mv2
Large mass, small velocity
small mass, large velocity
A 10 gram bullet moving at 700m/s and a 500kg rock rolling at 3m/s
have roughly the same amount of kinetic energy!
Survey Question
KE = 1/2 mv2
Which one of the following has the greatest
kinetic energy?
1) a 1 kg soccer ball moving at 4 m/s
2) a 100 kg anvil that is stationary
3) a 4 kg soccer ball moving at 2 m/s
4) a 5 kg soccer ball moving at 1 m/s
5) a 2 kg soccer ball moving at 3 m/s
Watch out for fast things!
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Damage in a car crash is proportional to v2.
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Trauma to head from falling anvil is proportional to v2
(or equivalently to how high it started from)
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A hurricane with 120 m.p.h. winds packs four times the
punch of a tropical storm with 60 m.p.h. winds.
Thermal Energy
n  Thermal
energy is another form of kinetic
energy (it is the motion of the atoms/
molecules in the object s material)
n  It is the lowest form of energy
n  A hot object has more thermal energy than
a cold object
Survey Question
The most energy inefficient thing you can do
while driving (assuming you are moving) is
1) to use your momentum to coast
up a hill
2) to have your headlights on
3) to run your air conditioner
4) to apply the brakes
5) to accelerate rapidly
Potential Energy
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What is Potential Energy?
¨  It
is the total amount of stored work an object (or you)
can potentially do.
¨  A rock held in your hand above the ground is storing
gravitational potential energy. If you let the rock go, the
potential energy is released in kinetic energy.
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Potential energy comes in different forms:
¨  Gravitational
potential energy (perched on a cliff)
¨  Chemical potential energy (e.g., a battery)
¨  Nuclear potential energy (stored in the nuclei of atoms)
¨  Mechanical potential energy (like a compressed spring)
¨  Electromagnetic potential energy (like when you hold two
magnets close to each other)
Gravitational Potential Energy
n  All
objects with mass attract each other
due to their gravitational force. Associated
with this force is a gravitational potential
energy:
Newton s constant
G M1 M2
Egrav =
d
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distance between
objects
For an object near the surface of the
Egrav = mgh
Earth:
The object s mass
The object s height
The acceleration due to gravity near the
surface of the Earth: g=9.8 m/s2
Kinetic and Potential Energy
Kinetic energy is associated with motion; a ball in motion
will have kinetic energy:
KE = ½ m v2
which can be derived by measuring its mass and velocity.
n  Potential energy is energy stored (e.g., water behind a
dam, a ball at the edge of a table, etc.); if the ball rolls
out of the table, the potential energy is converted to
kinetic energy. Gravitational potential energy is:
Eg = GMm/R
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Angular Momentum
and Its Conservation
Angular Momentum
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It is the `quantity of motion of a spinning (rotating)
object.
L = m . v . r = P . r (units: kg m2 s-1)
Depends on the geometry, the mass, and the rotational
velocity of an object.
Angular momentum is conserved.
¨  A
spinning wheel wants to keep spinning.
¨  A stationary wheel wants to keep still.
¨  Conservation is the tendency of a spinning object to keep
spinning with the rotation axis in a constant direction
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Angular momentum is also a vector quantity – this
means that the direction of the axis of rotation is
significant and resistant to change.
Everyday Examples of the
Conservation of Angular
Momentum
n  Riding
a bike
n  Spinning
a basketball on your finger
n  Steering
a satellite
n  A
spinning ice skater
Figuring out orbital velocities with
angular momentum
n  The
angular momentum of an object (like
a planet) moving in a circle (like an orbit!)
is:
L = m·v·r = constant
v
m = mass of planet
v = velocity of planet
r = orbital radius of planet
m
r
Kepler s Second Law of Orbits
2.
As a planet moves around it s orbit, the closer the
planet to the Sun, the higher its speed.
1 month
How to think about the conservation of
angular momentum.
The angular momentum before is equal to the
angular momentum afterwards.
For a planet or satellite:
Angular Momentum
when close
Angular Momentum
when distant
L1 = m1v1r1
L2 = m2v2r2
but L1 = L2
Since m1=m2,
v1r1 = v2r2
This is Kepler s Second
Law
Survey Question
L = m·v·r
If Earth orbited the Sun at a distance of ½
AU but with the same angular momentum
that it now has, how much faster/slower
would its orbital velocity be?
1) ¼ its current value
2) ½ its current value
3) the same as its current value
4) 2 times its current value
5) 4 times its current value