Ch10-1 Angular Position, Displacement, Velocity and Acceleration

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Chapter 10 Rotational Kinematics and Energy
Ch10-1 Angular Position, Displacement, Velocity
and Acceleration Rigid body every point on the
body moves through the same displacement and
rotates through the same angle.
? CCW
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CT1A ladybug sits at the outer edge of a
merry-go-round, and a gentleman bug sits halfway
between her and the axis of rotation. The
merry-go-round makes a complete revolution once
each second. The gentleman bugs angular speed
is A. half the ladybugs. B. the same
as the ladybugs. C. twice the ladybugs. D.
impossible to determine.
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Angular Position
Counterclockwise is positive
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Radians
? s/r (a dimensionless ratio)
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Angular Displacement
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Chapter 10 Rotational Kinematics and Energy
? CCW
Ch2-1 Angular Velocity
Average angular velocity ?av angular
displacement / elapsed time ?av
??/?t Instantaneous angular velocity ? lim
??/?t ?t 0
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P10.9 (p.308)
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Chapter 10 Rotational Kinematics and Energy
? CCW
Ch2-1 Angular Acceleration
Average angular acceleration ?av angular
velocity / elapsed time ?av
??/?t Instantaneous angular acceleration ?
lim ??/?t ?t 0
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Chapter 10 Rotational Kinematics and Energy
? CCW
Ch2-2 Rotational Kinematics
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• CT2 Which equation is correct for the fifth
  equation?
• ? ?0 ???
• ?2 ?02 ???
• ?2 ?0 ???
• ?2 ?02 2???

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Equations for Constant Acceleration Only

• v v0 at ? ?0 ?t
• vav (v0 v) / 2 ?av (?0 ?) / 2
• x x0 (v0 v) t / 2 ? ?0 (?0 ?) t /
  2
• x x0 v0 t at2/2 ? ?0 ?0 t ?t2/2
• v2 v02 2a(x x0) ?2 ?02 2?(? ?0)
• Assuming the initial conditions at t 0
• x x0 and ? ?0
• v v0 and ? ?0
• and a and ? are constant.

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1. ? ?0 ?t
2. ?av (?0 ?) / 2
3. ? ?0 (?0 ?) t / 2
4. ? ?0 ?0 t ?t2/2
5. ?2 ?02 2?(? ?0)

P10.20 (p.309) P10.22 (p.309)
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Chapter 10 Rotational Kinematics and Energy
Ch2-3 Connections Between Linear and Rotational
Quantities s r? vt r? at r? acp v2/r
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CT3 A ladybug sits at the outer edge of a
merry-go-round, and a gentleman bug sits halfway
between her and the axis of rotation. The
merry-go-round makes a complete revolution once
each second. The gentleman bugs linear speed
is A. half the ladybugs. B. the same
as the ladybugs. C. twice the ladybugs. D.
impossible to determine.
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P10-29 (p.310)
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• CT4 P10.29c The force necessary for Jeffs
  centripetal acceleration is exerted by
• gravity.
• Jeff.
• the vine.
• air resistance.

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Chapter 10 Rotational Kinematics and Energy
Ch2-4 Rolling Motion v r? if no slipping ? 0
if no friction
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Rolling Without SlippingConstant v and ?d
vt2?r vt (2?/t)r v ?r v recall that ?r
vt
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P10.45 (p.311)
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• CT5 P10.45b If the radius of the tires had been
  smaller, the angular acceleration of the tires
  would be
• greater.
• smaller.
• the same.

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Chapter 10 Rotational Kinematics and Energy
Ch2-5 Rotational Kinetic Energy and Moment of
Inertia For N particles I ?miri2 and K
I?2/2 Recall for translation K mv2/2 Both
translation and rotation K mv2/2 I?2/2
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Kinetic Energy of a Rotating Objectof Arbitrary
ShapeRigid Body of N Particles
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Table 10-1aMoments of Inertia for Uniform, Rigid
Objects of Various Shapes and Total Mass M
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Table 10-1bMoments of Inertia for Uniform, Rigid
Objects of Various Shapes and Total Mass M
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P10.52 (p.311)
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• CT6 P10.52b If the speed of the basketball is
  doubled to 2v, the fraction of rotational kinetic
  energy will
• double.
• halve.
• stay the same.

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Chapter 10 Rotational Kinematics and Energy
Ch2-6 Conservation of Energy WNC ?E with K
mv2/2 I?2/2
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Problem 10-60
P10.60 (p.311)
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• CT7 P10.60b If the radius of the bowling ball
  were increased, the final linear speed would
• increase.
• decrease.
• stay the same.

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• CT8 In the race between the hoop and solid disk,
  which will arrive at the base of the incline
  first?
• hoop.
• disk.
• neither, it will be a tie.