PHYS 218 sec. 517-520

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PHYS 218sec. 517-520

• Review
• Chap. 9
• Rotation of Rigid Bodies

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What you have to know

• Rotational kinematics (polar coordinate system)
• Relationship analogy between translational and
  angular motions
• Moment of inertia
• Rotational kinetic energy
• Section 9.6 is not in the curriculum.

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Analog between translation and rotation motion
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Angular velocity and acceleration
Angular velocity
The angular velocity and angular acceleration are
vectors. Follow the right hand rule.
Angular velocity
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Rotation with constant angular acceleration
All the formulas obtained for constant linear
acceleration are valid for the analog quantities
to translational motion
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Polar coordinate system
Therefore, this is valid in general.
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Polar coordinate system
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Energy in rotational motion
Rotational motion of a rigid body

• Depends on
• How the bodys mass is distributed in space,
• The axis of rotation

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Moment of inertia
Moments of inertia for various rigid bodies are
given in section 9.6
Rotational kinetic energy is obtained by summing
kinetic energies of each particles.
Each particle satisfies Work-Energy theorem
Work-Energy theorem holds true for rotational
kinetic energy
includes rotational kinetic energy
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Parallel-axis theorem
Moments of inertia depends on the axis of
rotation. There is a simple relationship between
Icm and IP if the two axes are parallel to each
other.
Two axes of rotation

1. If you know ICM, you can easily calculate IP.
2. IP is always larger than ICM. Therefore, ICM is
   smaller than any IP, and it is natural for a
   rigid body to rotate around an axis through its
   CM.

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Ex 9.8
Unwinding cable I
2m
final
initial
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Ex 9.9
Unwinding cable II
Kinetic energy of m
Rotational kinetic energy of M IMR2/2, wv/R
initial
final