What is Circular Motion?

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What is Circular Motion?
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Uniform Circular Motion

• Motion of an object travelling at constant speed
  in a circle
• Lets explore the kinematics of circular motion.
• Why is it accelerating, if the speed is constant?
• What would cause an object to move in a circle?

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What is Centripetal Force?

• Objects move in a straight line at a constant
  speed unless a force acts on them. This is
  Newton's First Law.
• However, many things move in curved paths,
  especially circles, and so there must be a force
  acting
• on them to pull them out
• of their straight line paths
• and make them turn
• corners.

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What Does Centripetal Force Depend On?

• We call the force that makes objects move in a
  circle the CENTRIPETAL FORCE(the name comes from
  Latin and means centre-seeking)
• How is Centripetal Force related to
• Mass of object?
• Velocity of object?
• Radius size of circle?
• Lets Explore!

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Uniform circular motion
The speed stays constant, but the direction
changes
v
R
The acceleration in this case is
called centripetal acceleration
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Wide turns and tight turns
little R
big R
for the same speed, the tighter turn requires
more acceleration
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Lets Determine the Velocity of an Object
Travelling in a Circle

• Remember Speed Distance/Time
• Lets define Period (T) as the time it takes the
  object to travel once around the circle.
• How far does it travel in one rotation?
• Therefore

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Ball on a string
The tension in the string provides the
necessary centripetal force to keep the ball
going in a circle.
path of ball if the string breaks
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Example

• What is the tension in a string used to twirl a
  0.3 kg ball at a speed of 2 m/s in a circle of 1
  meter radius?
• Force mass x acceleration m ? aC
• acceleration aC v2 / R (2 m/s)2/ 1 m
• 4 m/s2
• force m aC 0.3 ? 4 1.2 N
• If the string is not strong enough to handle this
  tension it will break and the ball goes off in a
  straight line.

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Motion On A Flat Curve

• On a flat, level curve, the friction between the
  tires and the road supplies the centripetal
  force.
• If the tires are worn smooth or the road is icy
  or oily, this friction force will not be
  available.
• The car will not be able to move in a circle, it
  will keep going in a straight line and therefore
  go off the road.

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Whats this Centrifugal force ? ?

• The red object will make the turn only if there
  is enough friction on it
• Otherwise it goes straight
• The apparent outward force is called the
  centrifugal force
• It is NOT A REAL force!
• An object will not move in a circle until
  something makes it, in this case the car door!

object on the dashboard
straight line object naturally follows
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What is Gravitational Force?

• Sir Isaac Newton discovered that every particle
  attracts every other particle in the universe
  with a force when he saw an apple fall from a
  tree towards the earth.
• The force of attraction between any two particles
  in the universe is called Gravitation or
  gravitational force

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Newtons Law of Universal Gravitation
G is the universal gravitational constant and
equals 6.673 x 10-11 N?m2 / kg2
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G vs. g

• Always distinguish between G and g
• G is the universal gravitational constant
• It is the same everywhere
• g is the acceleration due to gravity
• g 9.80 m/s2 at the surface of the Earth
• g will vary by location

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Why doesnt the moon fall into the earth?

• The moon is actually falling toward Earth but has
  great enough tangential velocity to avoid hitting
  Earth.
• If the moon did not fall, it would follow a
  straight-line path.

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Newtons Hypothesis
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Johannes Kepler

• 1571 1630
• German astronomer
• Best known for developing laws of planetary
  motion
• Based on the observations of Tycho Brahe

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Keplers Laws

• Keplers First Law
• All planets move in elliptical orbits with the
  Sun at one focus
• Keplers Second Law
• The radius vector drawn from the Sun to a planet
  sweeps out equal areas in equal time intervals
• Keplers Third Law
• The square of the orbital period of any planet is
  proportional to the cube of the semimajor axis of
  the elliptical orbit

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Keplers Third Law

• Can be predicted from the inverse square law
• Start by assuming a circular orbit
• The gravitational force supplies a centripetal
  force
• Ks is a constant

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Mass of the Sun

• Using the distance between the Earth and the Sun,
  and the period of the Earths orbit, Keplers
  Third Law can be used to find the mass of the Sun
• Similarly, the mass of any object being orbited
  can be found if you know information about
  objects orbiting it