1 Class #23 Centrifugal and Coriolis forces Accelerated reference frames Rotating reference frames Vector angular velocity Newton’s laws on rotating frame Two “fictitious forces”

2 Linearly Accelerated Reference Frames OK to use

3 Vector angular velocity Theta=90-Latitude = “CoLatitude” Earth obeys right-hand rule Omega points North  Earth spins clockwise  Sun rises in east A fixed vector “r” in rotating frame “S” appears to have a velocity “V” when seen from an inertial (non- rotating) frame S0. The velocity may be calculated from cross product of Omega as seen from S0 and “r” as seen in “S”.

4 Vector velocity – 1 minute problems Latitudes – Socorro – 34 N Nome, Alaska – 64 N Hilo, Hawaii – 19 N Hobart, Tazmania – 43 S What is circumferential velocity of each of these four cities? Spaceflight – A rocket needs a velocity of 8 km/s for orbit. What fraction is fuel use reduced if launch from equator instead of poles?

5 Vectors expressed in rotating frames Imagine same axes expressed in two frames S 0 stationary) and S (fixed to earth).

6 Derive Newton in rotating frame

7 Derive Newton in rotating frame II

8 Newton in a rotating frame Coriolis Term Centrifugal Term Newtonian Term

9 Coriolis force for a rocket going up is West

10 Problem L23-1 :30 A 100 kg weather rocket is launched straight up from Langmuir Lab. At t=10 sec, it’s velocity is 100 m/s. At t=100 sec, it’s velocity is 1000 m/s. What is the magnitude and direction of the Coriolis force at t=10 and 100 sec? An airplane flies due North from Albuquerque. Because of Coriolis force, the airplane will be deflected from its true North path A) Which direction will the deflection be in? B) How many miles off course will the airplane be after one hour? Assume v=300 m/s.