Physics 321

Physics 321 Hour 25 Accelerating Reference Frames II

Consider an accelerating train car

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

Handout rotation.nb Examples

Physics 321 Hour 26 Accelerating Reference Frames III

Velocities in Rotating Frames in S0 basis in S’ basis in S0 basis In S’ basis

Accelerations in Rotating Frames in S0 basis in S’ basis In S’ basis in S0 basis is the acceleration of the origin of S’ w.r.t S0

Forces in Rotating Frames Effective force in S’ Actual forces (in S’ basis) Transverse Coriolis Centrifugal Acceleration of origin

Effective force in S’ Actual forces (in S’ basis) Transverse Coriolis Centrifugal Forces on a Turntable

Polaris z0 x0,y0, z0 fixed in space x’, y’, z’ rotate with the earth The Earth z’ points outward x’ points east y’ points north z’ y’ y0 x’ x0

Polaris z0 λ The Earth z’ λ x0

Polaris z0 The Earth x0 Greatly exaggerated: The direction of is 90° from Polaris. The surface of the earth is perpendicular to .

Falling Stone • Ascending Missile • Air masses Applications of the Coriolis Force

Northern Hemisphere Low L