classical mechanics phys2006phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_24.pdf7 cannon shell...
TRANSCRIPT
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