Chapter 8: Dynamics II: Motion in a Plane

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Chapter 8 Dynamics II Motion in a Plane

• 8.2 Velocity and Acceleration in Uniform Circular
  
• Motion
• 8.3 Dynamics of Uniform Circular Motion
• 8.7 Nonuniform Circular Motion

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Stop to think 8.2 P 214Stop to think 8.3 P
219Stop to think 8.4 P 226Stop to think 8.5 P
228

• Example 8.3 P215
• Example 8.5 P217
• Example 8.6 P218
• Example 8.7 P227

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Velocity and Acceleration in UniformCircular
Motion
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Dynamics of Uniform Circular Motion

• From the Newtons second law, a particle of mass
  m moving at constant speed V around a circle of
  radius r must have a net force of
• magnitude (mV2/r) pointing toward the center
  of the circle

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Ex. 8.3 Spinning in a circle

• An Energetic father places his 20 Kg child on a
  5.0Kg cart to which a 2.0-m-long rope is
  attached. He then holds the end of the rope and
  spins the cart and child around in a circle,
  keeping the rope parallel to the ground. If the
  tension in the rope is 100N, how many revolutions
  per minute (rpm) does the cart make?

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The Conical Pendulum
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Problem 46 Mass m1 on the frictionless table is
connected by a string through a hole in the table
to a hanging mass m2. With what speed must m1
rotate in a circle of radius r if m2 is to remain
hanging at rest?

• If m2 remains hanging at rest
• T-m2g0
• (2) For m1, N m1g
• T m1 V2 /r

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A roller coaster car going around a vertical
loop-the loop of radius r. Well assume that the
motion makes a complete circle and not worry
about the entrance to and exit from the loop. Why
doesnt the car fall off at the top of the circle
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Nonuniform Circular Motion
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Problem 8.62, A small ball rolls around a
horizontal circle at height y inside a
frictionless hemispherical bowl of radius R.,
find an expression for the balls angular
velocity in terms of R, y, g