Physics 321
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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

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Physics 321

Physics 321

Hour 24

Accelerating Reference Frames I


Consider an accelerating train car

Consider an accelerating train car


Examples

  • Glass of water in a car

  • Tides

Examples


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


Proof

Proof


Proof1

Proof


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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