Dynamics of Uniform Circular Motion

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Dynamics of Uniform Circular Motion
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Dynamics of Uniform Circular Motion

• Uniform circular motion is the motion of an
  object traveling at a constant speed on a
  circular path
• The period T is the time required for the object
  to travel once around the circle
• The speed v of the object is related to the
  period and the radius of the circle by
• Example 1 and 2 page 125-126

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Dynamics of Uniform Circular Motion

• Centripetal Acceleration
• An object in uniform circular motion experiences
  an acceleration (because its direction is
  changing), known as centripetal acceleration. The
  magnitude of the centripetal acceleration is
• where v is the speed of the object, and r is the
  radius of the circle. Example 3 page 127

ac is always pointing toward the center of the
circle
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Dynamics of Uniform Circular Motion

• Centripetal Force
• To produce a centripetal acceleration, a net
  force pointing towards the center of the circle
  is neededrememberFma....aF/m
• where m is the mass of the object, v is the speed
  of the object, and r is the radius of the circle.
  
• Example 5 and 7 page 129

acceleration
As v increases, so will the tension in the string
(Fc)
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Dynamics of Uniform Circular Motion

• Centripetal force and Centrifugal force are the
  action-reaction force pair associated with
  circular motion.
• According to Newton's first law of motion, a
  moving body travels along a straight path with
  constant velocity unless it is acted on by an
  outside force.
• For circular motion to occur there must be a
  constant force acting on a body, pushing it
  toward the center of the circular path
• This force is the centripetal (center-seeking)
  force
• For a planet orbiting the sun, the force is
  gravitational
• an object twirled on a string, the force is
  mechanical
• for an electron orbiting an atom, it is
  electrical
• According to Newton's third law of motion, for
  every action there is an equal and opposite
  reaction. The centripetal force, the action, is
  balanced by a reaction force, the centrifugal
  (center-fleeing) force. The two forces are
  equal in magnitude and opposite in direction. The
  centrifugal force does not act on the body in
  motion the only force acting on the body in
  motion is the centripetal force.
• The centrifugal force acts on the source of the
  centripetal force to displace it radially from
  the center of the path. Thus, in twirling a mass
  on a string, the centripetal force transmitted by
  the string pulls in on the mass to keep it in its
  circular path, while the centrifugal force
  transmitted by the string pulls outward on its
  point of attachment at the center of the path.
• The centrifugal force is often mistakenly thought
  to cause a body to fly out of its circular path
  when it is released rather, it is the removal of
  the centripetal force that allows the body to
  travel in a straight line as required by Newton's
  first law.

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Applications of Dynamics of Uniform Circular
Motion

• Banked Curves
• The components of the normal force
• Do example 8 page 132

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Dynamics of Uniform Circular Motion

• Banked Curves simulation

Centripetal force
90kg
This block doesnt
This block moves
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Vertical Circular Motion and Roller Coasters!