Physics 321

Hour 24Accelerating Reference Frames I

Bottom Line• In linear systems, we have to add a term to

Newton’s 2nd Law to account for the acceleration of the frame.

is the perceived acceleration is the true force is the acceleration of the frame

• In rotating frames, we can replace time derivatives with … expressions.

Consider an accelerating train car∫0

𝑡

𝑣𝑑~𝑡𝑥 (𝑡)

𝑥0(𝑡)𝑣 (𝑡)

Examples• Glass of water in a car• Tides

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.)

Angular Velocity• Angular velocity vector (r.h.r.) • Let be a unit vector fixed in a body

• In particular

• In general

Transforming Velocity˙⃗𝑟0= ˙⃗𝑟+ (Ω⃗×𝑟 )𝑆