Uniform Circular Motion

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Uniform Circular Motion

• Physics 12

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Centripetal Acceleration

• In order for an object to follow a circular path,
  a force needs to be applied in order to
  accelerate the object
• Although the magnitude of the velocity may remain
  constant, the direction of the velocity will be
  constantly changing
• As a result, this force will provide a
  centripetal acceleration towards the centre of
  the circular path

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How can we calculate centripetal acceleration?
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Centripetal Force

• Like the centripetal acceleration, the
  centripetal force is always directed towards the
  centre of the circle
• The centripetal force can be calculated using
  Newtons Second Law of Motion

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Problem horizontal circle

• A student attempts to spin a rubber stopper (m
  0.050kg) in a horizontal circle with a radius
  of 0.75m. If the stopper completes 2.5
  revolutions every second, determine the
  following
• The centripetal acceleration
• The centripetal force

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• The stopper will cover a distance that is 2.5
  times the circumference of the circle every
  second
• Determine the circumference
• Multiply by 2.5
• Use the distance and time (one second) to
  calculate the speed of the stopper

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• Use the speed and radius to determine the
  centripetal acceleration
• Then use the centripetal acceleration and mass to
  determine the centripetal force

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Problem vertical circle

• A student is on a carnival ride that spins in a
  vertical circle.
• Determine the minimum speed that the ride must
  travel in order to keep the student safe if the
  radius of the ride is 3.5m.
• Determine the maximum force the student
  experiences during the ride (in terms of number
  of times the gravitational force)

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Problem vertical circle
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Vertical Circle

• While travelling in a vertical circle, gravity
  must be considered in the solution
• While at the top of the circle, gravity acts
  towards the centre of the circle and provides
  some of the centripetal force
• While at the bottom of the circle, gravity acts
  away from the centre of the circle and the force
  applied to the object must overcome both gravity
  and provide the centripetal force

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Vertical Circle

• To determine the minimum velocity required, use
  the centripetal force equal to the gravitational
  force (as any slower than this and the student
  would fall to the ground)
• To determine the maximum force the student
  experiences, consider the bottom of the ride when
  gravity must be overcome

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• At the top of the circle, set the gravitational
  force (weight) equal to the centripetal force
• Solve for velocity

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• At the bottom of the circle, the net force is
  equal to the sum of the gravitational force and
  the centripetal force
• Solve for number of times the acceleration due to
  gravity

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Road Design

• You are responsible to determine the speed limit
  for a turn on the highway. The radius of the
  turn is 55m and the coefficient of static
  friction between the tires and the road is 0.90.
• Find the maximum speed at which a vehicle can
  safely navigate the turn
• If the road is wet and the coefficient drops to
  0.50, how does this change the maximum speed

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Diagrams
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The maximum speed at which a vehicle can safely
navigate the turn
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Coefficient drops to 0.50, how does this change
the maximum speed
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The Motion of Planets

• Birth of Modern Astronomy
• OR
• How Nerds Changed the World!!!

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Learning Outcomes (Students will be able to)