classical mechanics phys2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 cannon shell...
TRANSCRIPT
![Page 1: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/1.jpg)
PHYS 2006
Tim Freegarde
Classical Mechanics
24 Coriolis examples2020-21
![Page 2: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/2.jpg)
2
Rotating coordinate systems
• local coordinates not an inertial frame
• ‘ficticious’ forces: • centrifugal
• Coriolis
![Page 3: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/3.jpg)
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
![Page 4: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/4.jpg)
4
Cannon shell
![Page 5: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/5.jpg)
5
Cannon shell
![Page 6: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/6.jpg)
6
Cannon shell
![Page 7: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/7.jpg)
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
![Page 8: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/8.jpg)
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
![Page 9: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/9.jpg)
9
Foucault’s pendulum
![Page 10: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/10.jpg)
10
Foucault’s pendulum
![Page 11: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/11.jpg)
11
Foucault’s pendulum
![Page 12: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/12.jpg)
12
Foucault’s pendulum
![Page 13: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/13.jpg)
13
Foucault’s pendulum
![Page 14: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/14.jpg)
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
![Page 15: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/15.jpg)
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
![Page 16: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/16.jpg)
16
Geostrophic wind
![Page 17: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/17.jpg)
17
Geostrophic wind
Lpressuregradient
Coriolis
![Page 18: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/18.jpg)
18
Geostrophic wind
![Page 19: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/19.jpg)
Geostrophic wind
19
• isobars: pressure contours (4 hPa)• cold/warm fronts divide air masses
GEOSTROPHIC WIND
• closer isobars→ higher Coriolis force→ stronger wind
![Page 20: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/20.jpg)
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)
![Page 21: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/21.jpg)
21
Vibrating structure gyroscope
Grewal, Weill & Andres,Global Positioning Systems, Inertial Navigation
and Integration (2007)
![Page 22: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/22.jpg)
22
Vibrating structure gyroscope
Grewal, Weill & Andres,Global Positioning Systems, Inertial Navigation
and Integration (2007)
Drosophila melanogaster, Shwetha Mureli
![Page 23: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/23.jpg)
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
![Page 24: Classical Mechanics PHYS2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 Cannon shell fired north •velocity varies during trajectory •Coriolis correction hence changes](https://reader033.vdocuments.us/reader033/viewer/2022060906/60a12187a6e7e169464dd23a/html5/thumbnails/24.jpg)
PHYS 2006
Tim Freegarde
Classical Mechanics