1. 1 Centrifugal and Coriolis forces Read Ch 9 – Next HW Due Tues 11/11 [L14-1,9.1, 9.2,9.3, 9.8, 9.11, 9.16, 9.18] Accelerated reference frames (last time) Rotating reference frames Vector angular velocity Newton’s laws on rotating frame Two “fictitious forces” DVD on Ref frames

2. 2 Linearly Accelerated Reference Frames OK to use

3. 3 Vector angular velocity In English; velocity of a point “A” seen from an inertial reference frame may be calculated by crossing the rotational velocity with the fixed vector pointing to “A” in the rotating frame. Theta=90-Latitude = “CoLatitude” Omega points North  Earth spins clockwise  Sun rises in east

4. 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. 5 Vectors expressed in rotating frames Imagine same axes (x,y,z) expressed in two frames S 0 stationary) and S (fixed to earth).

6. 6 Derive Newton in rotating frame

7. 7 Derive Newton in rotating frame II

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

9. 9 Alternate form of Left-Hand Rule

10. 10 Coriolis force for a rocket going up is West

11. 11 Problem L14-1 :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.

12. 12 Tides :55 Why are there bulges on BOTH sides of the earth?

13. 13 Windup