# Physics 321 - PowerPoint PPT Presentation

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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

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