Physics 321

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# Physics 321 - PowerPoint PPT Presentation

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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Presentation Transcript

### 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.
• (Complex rotations can be taken to be a series of infinitesimal rotations.)
• Tiny rotations commute.
• (Larger rotations do not commute.)

### Proof

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 vector (r.h.r.)

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