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Physics 321. Hour 24 Accelerating Reference Frames I. Consider an accelerating train car. Glass of water in a car Tides. Examples. Euler’s Theorem Any tiny rotation can be considered as a rotation about a fixed axis.

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physics 321

Physics 321

Hour 24

Accelerating Reference Frames I

two angular momentum theorems

Euler’s Theorem

  • Any tiny rotation can be considered as a rotation about a fixed axis.
  • (Complex rotations can be taken to be a series of infinitesimal rotations.)
  • Tiny rotations commute.
  • (Larger rotations do not commute.)

Two Angular Momentum Theorems

proof2

Any unit vector can be written as

In general

where S0 is the lab (inertial) frame and S’ is a frame rotating with angular velocity .

Proof

angular velocity

Angular velocity vector (r.h.r.)

  • Let be a unit vector fixed in a body
  • In particular
  • In general

Angular Velocity

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