PHYS 2006

Tim Freegarde

Classical Mechanics

24 Coriolis examples2020-21

2

Rotating coordinate systems

• local coordinates not an inertial frame

• ‘ficticious’ forces: • centrifugal

• Coriolis

3

Rotating coordinate systems

inertial frame local, rotating frame

• differentiate twice, taking into account variation of local (rotating) unit vectors

Coriolis centrifugal

'

'

'

• in local coordinate frame , this becomes

4

Cannon shell

5

Cannon shell

6

Cannon shell

7

Cannon shell fired north

• velocity varies during trajectory

• Coriolis correction hence changes direction along the shell’s path

small

large

• more significant towards end of trajectory in this case

• if air resistance slows shell:

EXPECTED TRAJECTORY CORIOLIS DEFLECTION

for given range: descent speed lower, butdescent duration longer

8

Cannon shell

• velocity varies during trajectory

• Coriolis correction hence changes direction along the shell’s path

• more significant towards end of trajectory in this case

• if air resistance slows shell:for given range: descent speed lower, but

descent duration longer

EXPECTED TRAJECTORY CORIOLIS DEFLECTION

9

Foucault’s pendulum

10

Foucault’s pendulum

11

Foucault’s pendulum

12

Foucault’s pendulum

13

Foucault’s pendulum

Coriolis effect

14

460 m s-1

300 m s-1

H

L

• tendency to turn right in N hemisphere

• to observer moving with Earth, appears as virtual force

• pressure gradient balances Coriolis & centrifugal forces

• at altitude, flow follows isobars around high/low pressure

Lpressuregradient

Coriolis

Buys-Ballot’s law

15

460 m s-1

300 m s-1

H

L

• with the wind on your back,in the N hemisphere,the low pressure is on the left

Lpressuregradient

Coriolis

Low High

16

Geostrophic wind

17

Geostrophic wind

Lpressuregradient

Coriolis

18

Geostrophic wind

Geostrophic wind

19

• isobars: pressure contours (4 hPa)• cold/warm fronts divide air masses

GEOSTROPHIC WIND

• closer isobars→ higher Coriolis force→ stronger wind

20

Vibrating structure gyroscope

Grewal, Weill & Andres,Global Positioning Systems, Inertial Navigation

and Integration (2007)

Weinberg, Bernstein, Cho, King, Kourepenis, Ward & Sohn,Int Conf Gyrosc Technol & Nav (2), 9-87 (1995)

21

Vibrating structure gyroscope

Grewal, Weill & Andres,Global Positioning Systems, Inertial Navigation

and Integration (2007)

22

Vibrating structure gyroscope

Grewal, Weill & Andres,Global Positioning Systems, Inertial Navigation

and Integration (2007)

Drosophila melanogaster, Shwetha Mureli

23

Vibrating structure gyroscope

Grewal, Weill & Andres,Global Positioning Systems, Inertial Navigation

and Integration (2007)

Life on Earth, BBC (1979)

• F W Meredith, Control of equilibrium in the flying insect, Nature 163, 74 (1949)

• Michael Dickinson, How a fly flies, TED www.youtube.com/watch?v=e_44G-kE8lE

PHYS 2006

Tim Freegarde

Classical Mechanics