66 Pages·2012·2.25 MB·English

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Chap. 6: Angular Momentum and Fixed Axis Rotation R i s h i k e s h V a i d y a Theoretical Particle Physics Oﬃce: 3265 [email protected] Physics Group, B I T S Pilani September 7, 2012 Outline Introduction 1 Angular Momentum as a Pseudo (or Axial) Vecto 2 Torque as a Pseudo Vector 3 Moment of Inertia & Dynamics of Pure Rotation 4 Translation + Rotation 5 Work Energy Theorem 6 What is Rotation 1-Dim World: Concept of direction (and hence vectors) meaningless. Magnitudes suﬃciently characterize physical quantities. A change is only a change in magnitude. What is Rotation 2-Dim World: Inﬁnitely many directions and hence the concept of vectors. Vectors can change in two ways. Pure Scaling: Changes in magnitude only (∆r) Pure Rotation: Changes in direction only (∆θ) Rotation quantiﬁes pure change in direction Translation and Rotation Translation and Rotation Pure translation: The line connecting any two particles of body retains its direction in space. Translation and Rotation Pure Rotation: The trajectories of all points of the body are circles whose centers lie in a common straight line called the axis of rotation. Translation and Rotation Translation and Rotation Angular Momemtum as a Pseudo (or Axial) Vector If ~r and ~p are in x − y plane and φ is angle between them: ~ ˆ L =~r ×~p = rp sin φk |L | = r p = p r z ⊥ ⊥

Angular Momentum and Fixed Axis Rotation railroad car which is going around an For ﬁxed axis rotation:

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