Download 3 5-1 Kinematics of Uniform Circular Motion

Chapter 5
Circular Motion &
Gravitation
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5-1 Kinematics of Uniform Circular Motion
Uniform circular motion: motion in a circle of
constant radius at constant speed
Instantaneous velocity is always tangent to circle.
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 Although the magnitude of the velocity may remain
constant the direction of the velocity is constantly
changing
 Recall that acceleration is the change in velocity over
the change in time and is a vector
 In circular motion, the direction is constantly
changing which means an object moving in circular
motion is ALWAYS accelerating, even if it’s velocity
remains constant
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5-1 Kinematics of Uniform Circular Motion
In circular motion acceleration is called
centripetal, or radial, acceleration, aR and it points
towards the center of the circle.
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5-1 Kinematics of Uniform Circular Motion
The magnitude of aR can be found by the formula
(5-1)
aR and v are
always
perpendicular to
each other
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5-2 Dynamics of Uniform Circular Motion
For an object to be in uniform circular motion, there
must be a net force acting on it; a centripetal force
We know that
We just saw that aR is
so we can say the
rotational force is
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(5-1)
5-2 Dynamics of Uniform Circular Motion
There is no centrifugal force pointing outward; only
the natural tendency of the object to move in a
straight line.
If the centripetal force vanishes, the object flies off
tangent to the circle.
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5-3 Highway Curves, Banked and Unbanked
If the frictional force is
insufficient, the car will
tend to move more nearly
in a straight line, as the
skid marks show.
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5-6 Newton’s Law of Universal Gravitation
If the force of gravity is being exerted on objects on
Earth, what is the origin of that force?
Newton’s realization was
that the force must come
from the Earth.
He further realized that this
force must be what keeps
the Moon in its orbit.
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5-6 Newton’s Law of Universal Gravitation
 By observing planetary orbits Newton proposed his
law of Law of Universal Gravitation
 Every particle in the universe attracts every other
particle
 This force acts along the line joining the two
particles
Where G is a universal constant
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5-9 Kepler’s Laws and Newton's Synthesis
 Even before Newton, Johannes Kepler studied and
described the motion of the planets (1571-1630)
 His findings are now summarized in Kepler’s laws
of planetary motion
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Kepler’s first law
 The path of each planet around the Sun is an
ellipse with the sun at one focus
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Kepler’s second law
 Each planet moves so that an imaginary line drawn
from the Sun to the planet sweeps out equal areas in
equal periods of time
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Kepler’s third law
 The ratio of the squares of the period T of any 2
planets revolving around the Sun is equal to the
ratio of the cubes of their mean distances s from the
Sun
 T is the period and r is the orbit radius
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5-10 Types of Forces in Nature
 Modern physics currently recognizes four fundamental
forces:
1.
Gravity
2. Electromagnetism (sometimes combined with the weak
nuclear force and called the Electroweak force)
3. Weak nuclear force (responsible for some types of
radioactive decay)
4. Strong nuclear force (binds protons and neutrons together
in the nucleus)
 Other everyday observations (such as friction) are
not fundamental forces, but one of these four
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5-10 Types of Forces in Nature
 So far we’ve only talked about gravity; the weakest of the 4
forces
 Other forces will come up as the year progresses
 Physicists have been working on trying to unify these
theories into one grand unified theory, or GUT. Also
called the theory of everything or TOE.
 TOE and GUTs are very popular and controversial in
physics!
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References
 Giancoli, Douglas. Physics: Principles with Applications 6th
Edition. 2009.
 Zitewitz. Physics: Principles and Problems. 2004
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