PHY 711 Fall 2014 -- Lecture 24 110/22/2014

PHY 711 Classical Mechanics and Mathematical Methods

10-10:50 AM MWF Olin 103

Plan for Lecture 24:Rotational motion (Chapter 5)

1. Rigid body motion2. Moment of inertia tensor

PHY 711 Fall 2014 -- Lecture 24 210/22/2014

PHY 711 Fall 2014 -- Lecture 24 310/22/2014

PHY 711 Fall 2014 -- Lecture 24 410/22/2014

PHY 711 Fall 2014 -- Lecture 24 510/22/2014

The physics of rigid body motion; body fixed frame vs inertial frame:

PHY 711 Fall 2014 -- Lecture 24 610/22/2014

Comparison of analysis in “inertial frame” versus “non-inertial frame”

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system coordinate moving a ˆby Denote

system coordinate fixed a ˆby Denote

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PHY 711 Fall 2014 -- Lecture 24 710/22/2014

Properties of the frame motion (rotation):

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PHY 711 Fall 2014 -- Lecture 24 810/22/2014

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PHY 711 Fall 2014 -- Lecture 24 910/22/2014

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:body rigid ofenergy Kinetic

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PHY 711 Fall 2014 -- Lecture 24 1010/22/2014

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PHY 711 Fall 2014 -- Lecture 24 1110/22/2014

x

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: tensorinertia ofMoment

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PHY 711 Fall 2014 -- Lecture 24 1210/22/2014

Properties of moment of inertia tensor: Symmetric matrix real eigenvalues I1,I2,I3

orthogonal eigenvectors3,2,1 ˆˆ iI iii eeI

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PHY 711 Fall 2014 -- Lecture 24 1310/22/2014

Changing origin of rotation ''''

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mp

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PHY 711 Fall 2014 -- Lecture 24 1410/22/2014

2' 2CMjijCMiijCMjiijijij rRRrMRRRMII Rr

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and ˆˆˆ that Suppose

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PHY 711 Fall 2014 -- Lecture 24 1510/22/2014

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PHY 711 Fall 2014 -- Lecture 24 1610/22/2014

Descriptions of rotation about a given origin

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PHY 711 Fall 2014 -- Lecture 24 1710/22/2014

Descriptions of rotation about a given origin -- continued

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PHY 711 Fall 2014 -- Lecture 24 1810/22/2014

Descriptions of rotation about a given origin -- continued

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momentumangular of change of rate Time

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PHY 711 Fall 2014 -- Lecture 24 1910/22/2014

Descriptions of rotation about a given origin -- continued

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equation torque that theNote

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PHY 711 Fall 2014 -- Lecture 24 2010/22/2014

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(constant)~ 0~0~~~0~~~

: -- topsymmetricfor Solution

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PHY 711 Fall 2014 -- Lecture 24 2110/22/2014

Solution of Euler equations for a symmetric top -- continued

)sin()(~ )cos()(~ :Solution

~ where

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PHY 711 Fall 2014 -- Lecture 24 2210/22/2014

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