Examples in Chapter 9

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Examples in Chapter 9
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9.25

• A flywheel with a radius of 0.3 m starts from
  rest and accelerates with a constant angular
  acceleration of 0.6 rad/s2 . Compute the
  magnitude of
• the angular accleration
• the radial acceleration
• The resultant acceleration of a point on its rim
• At the start
• After it has turned through 600
• After it has turned through 1200

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Starting conditions

• a 0.3 rad/s
• w0 0
• r 0.3 m

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Equations to think about
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At the start
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At 600
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At 1200
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9.46

• A light flexible rope is wrapped several times
  around a hollow cylinder with a weight of 40 N
  and a radius of 0.25 m that rotates without
  friction about a fixed horizontal axis. The
  cylinder is attached is attached to the axle by
  spokes of a negligible moment of inertia. The
  cylinder is initially at rest. The free end of
  the rope is pulled with a constant force P for a
  distance of 5 m at which the end of the rope is
  moving at 6 m/s. If the rope does not slip on the
  cylinder, what is the value of P?

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Some figurin

• WDR
• Where R ½ I w2
• vrw or v/rw
• Initially, w0 0 so DR ½ I (v/r)2
• From Imr2(40 N/9.8)(.25)20.255
• WFd or P(5 m)
• W5P
• P (1/2)0.255(6/.25)2/514.7 N

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9.71

• A vacuum cleaner belt is looped over a shaft of
  radius 0.45 cm and a wheel of radius 2.0 cm .
  The arrangement is shown below. The motor turns
  the shaft at 60 rev/s and the shaft is connected
  to a beater bar which sweeps the carpet. Assume
  that the belt doesnt slip.
• What is the speed of a point on the belt?
• What is the angular velocity of the belt?

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Some more figurin

• Part a) vrw where
• r0.45 cm
• w 60 rev/s (2p radians/rev)377 rad/s
• v0.45377169 cm/s or 1.69 m/s
• Part b) w2 169 cm/s / 2 cm 84.8 rad/s

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Hint on 9.72

• The wheels are coupled so that there is the
  tangential velocity is constant so that
• w1/w2 r2/r1