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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.)

Two Angular Momentum Theorems

Proof

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

Angular Velocity

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