Circular Motion

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Circular Motion

• Angular Acceleration

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Distance around a Circle

• Circumference
• Distance around a circle

r
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Period and Frequency

• The period is the time it takes an object in
  uniform circular motion to complete one
  revolution of the circle.
• The frequency is how many revolutions an object
  in uniform circular motion completes in one
  period.
• Relationship between period and frequency
• T1/f
• F1/T (unit are hertz, Hz, which is 1/second)

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Speed, Velocity, Angular Velocity
W.S. Ratios cmtp 7

• Omegar ?r

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Centripetal Acceleration

• Centripetal Acceleration
• Acceleration due to the centripetal acceleration
• If an object is moving in a circular motion, it
  is experiencing centripetal acceleration relative
  to the plane of circular motion.

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Centripetal Force

• A way to describe what a force is doing. Normal
  force, gravity, tension - each of these forces
  can be a centripetal force if it is causing an
  object to move in uniform circular motion.  

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Centripetal Acceleration vs. Acceleration of
Gravity

• G-force, how many gs
• Multiple of gravity,
• Vacuum at 600rpm, r 10cm
• Find T in seconds or f in Hz
• Centrifuge at 2000rpm, r 15cm
• Find T in seconds or f in Hz

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Relative Motion

• Velocity of A relative to B
• Velocity of B relative to C
• Velocity of A relative to C
• Must add Velocity of A (relative to B) and
  Velocity of B (relative to C) together.

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Vector Math

• a) Draw a picture showing the way the two
  vectors add together
• b) Break any vectors at angles into x and y
  components
• c) Add the x components to find the total
  displacement component along that axis
• d) Add the y components to find the total
  displacement component along that axis
• e) Add the total x and y components to find the
  total displacement
• Show work for each step.

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Planet Avg Radius Period (T) Angular acceleration
Mercury 57.9 0.241 39.4
Venus
Earth 150 1 5.92
Mars
Jupiter 778 11.9 0.217
Saturn
Uranus
Neptune
Pluto 5890 248 0.0038
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Centripetal acceleration vs. mean radius
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Centripetal acceleration vs. mean radius
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Centripetal Force

• Q No force is required for an object to move in
  uniform circular motion. After all, its speed is
  constant.
• A Speed is constant, but its velocity is
  changing due to its change in direction, which
  means it is accelerating. By Newtons second law,
  this means there must be a net force causing this
  acceleration.

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Summary

• Uniform circular motion is movement in a circle
  at a constant speed. But while speed is constant
  in this type of motion, velocity is not. Since
  instantaneous velocity in uniform circular motion
  is always tangent to the circle, its direction
  changes as the object's position changes.

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Summary

• The period is the time it takes an object in
  uniform circular motion to complete one
  revolution of the circle.
• The frequency is how many revolutions an object
  in uniform circular motion completes in one
  period.
• T1/f
• F1/T

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Summary

• Since the velocity of an object moving in uniform
  circular motion changes, it is accelerating. The
  acceleration due to its change in direction is
  called centripetal acceleration. For uniform
  circular motion, the acceleration vector has a
  constant magnitude and always points toward the
  center of the circle.

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Summary

• Newton's second law can be applied to an object
  in uniform circular motion. The net force causing
  centripetal acceleration is called a centripetal
  force. Like centripetal acceleration, it is
  directed toward the center of the circle.

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Summary

• A centripetal force is not a new type of force
  rather, it describes a role that is played by one
  or more forces in the situation, since there must
  be some force that is changing the velocity of
  the object. For example, the force of gravity
  keeps the Moon in a roughly circular orbit around
  the Earth, while the normal force of the road and
  the force of friction combine to keep a car in
  circular motion around a banked curve.

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Homework

• Chapter 6
• Projectile Motion
• 4, 5, 6, 10
• 32, 34, 35, 36, 45, 61, 63, 64,65
• When calculating time an object is in the air,
  consider the final height or displacement in the
  y direction. That is, how high is it when it is
  laying on the ground.