Circular Motion: Problem Solving

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Circular Motion Problem Solving

• 8.01
• W04D3

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Todays Reading Assignment W04D3

• Problem Solving Strategy Circular Motion Dynamics

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Concept Question Tension and String Theory

• A ball is suspended from a vertical rod by
  two strings of equal strength and equal length.
  The strings are very light and do not stretch.
  The rod is spun with a constant angular
  acceleration. Which string breaks first?
• the upper string
• the lower string
• they break simultaneously
• cannot tell without more information

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Group Problem Tension and String Theory

• A ball of mass m is suspended from a
  vertical rod by two strings of equal strength and
  equal length l. The strings are very light and do
  not stretch. The rod is spun with a constant
  angular speed ?. What are the tensions in the two
  strings?

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Group Problem Tension in Strings

• Two objects of equal mass m are whirling around
  a shaft with a constant angular velocity ?. The
  first object is a distance d from the central
  axis, and the second object is a distance 2d
  from the axis. You may ignore the mass of the
  strings and neglect the effect of gravity. What
  are tensions in the string between the inner
  object and the outer object and the string
  between the shaft and the inner object?

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Group Problem Tension in a Spinning Rope
A uniform rope of mass m and length L is
attached to shaft that is rotating at constant
angular velocity ?. You may ignore the effect of
gravitation.

• a) Divide the rope into small pieces of length
  ?r. Consider the piece located a distance r from
  the shaft. Draw a free body force diagram on that
  small piece.
• b) Apply Newtons Second Law to that small piece
  and find in the limit as ?r approaches zero, a
  differential equation relating dT/dr to the
  distance r from the shaft.
• c) Integrate the differential equation you found
  in part b) to find the tension in the rope as a
  function of distance from the shaft.

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Next Reading Assignment W05D1

• Young and Freedman 6.1-6.4
• Review Module Scalar Product