Gróf Andrea

Karinthy Frigyes Gimnázium, Budapest

Description of motions

PHYSICS

•Choice of referenceframe emphasized.•But inertial frames usedexclusively.•Students corrected byteacher if they talk aboutcentrifugal force.

GEOGRAPHY

•Idea of reference frame not addressed.•"Natural" reference frame is non-inertial.•Explanations refer tocentrifugaland Coriolis forces.

1. Survey on the understanding of

the physics behind geography

2. A possible introduction to inertial

forces:

merry-go-round example treated

quantitatively

3. Applications in physics and

geography

!

1. Survey on the physics (mechanics) behind

geography

MCQ questions on timekeeping, the shape of the Earth,

motions of air and the seas, tides, etc.

215 students (16 and 17-year olds)

Background: 1 year of physical geography

and 1 year of physics

A.Fcentrifugal << Fcentripetal for fast rotations 11%

B. Fcentrifugal only exists for astronomical sizes 10%

C. Observer does/does not rotate along 17%

D.Fcentrifugal always present, therefore not felt 49%

(no answer 13%)

Questions involving inertial forces

Q

A

Geography: oblate Earth explained in terms of the

centrifugal force.

Physics problems on rotating objects: such forces not

considered.

What is the difference?

N

?Q

S

??

Q

A.South clockwise, north counterclockwise 56%

B. North clockwise, south counterclockwise 21%

C. Same sense 8%

D.Anything may happen 10%

(no answer 5%)

A

https://www.youtube.com/watch?v=4llVfoDuVlw

s

m14.3

3

5.122

T

rv

2

2

2

s

m58.6 r

r

va

N13268.520 maF

A

B

2. Describing motions on a playground

roundabout

The motion of A as seen by B:

s

m64.35.014.3

N177.084.802.0merrynet

maFF

2

22

s

m84.8

5.1

64.3)(

r

uva

Tangential motion as described by the inertial observer B

For rotating observer A:

,s

m17.0

5.1

5.0

2

22

r

ua

0.177NN003.017.002.0net

maF

What other force is there?

FcfFcoriolis

Fmerry= 0.177N

N003.0net

F N132.0cfF

N 042.0

132.0177.0003.0

N177.0merry

F

(inwards)

(inwards)

(outwards)

needed:

(outwards)

r

uvmmaFF

2

merrynet

)(

r

mu

r

mvu

r

mv22

2

r

mvu

r

mvF

r

mu 22

merry

2

0.003 N = 0.177 N – 0.132 N – 0.042 N.

umur

vm

r

mvu 22

2

N042.05.1

5.014.302.02

maFnet

For B

For A

Algebraically:

Fcf

Fcoriolis

Fmerry= 0.177N

For B

a = 0

A

B

ω

The same motion as seen by A:

Radial speed constant

Tangential speed

increasest

rv

t t

trs

trta 2

)(2

1

vt

ra

22

t

t

t

Latitude of Budapest: φ = 47.5º

(a) Magnitude and direction of

the centrifugal acceleration

in Budapest.

(b) Magnitude and direction of the

acceleration of free fall in Budapest?

mgFgrav

Ω

Fcf

(local) verticalWhich way is "down"?

Sports events?

(a) Gravitational, centrifugal acceleration and free

fall acceleration at the Equator?

(b) Athlete can jump to 8 metres at the poles. How

far can he jump on the Equator?

3. Applications: Inertial forces

on the rotating Earth

Coriolis force at the Equator

Air moving at u = 20 m/s towards the west.

Magnitude of acceleration towards the centre of the Earth?

(a) according to an inertial observer?

(b) according to an Earth-based observer?

(c) What is the magnitude and direction of the Coriolis

acceleration?

6

2652

1038.6

20)1038.6)(1029.7()(

R

uRa

2m/s 0369.0

25

6

22

m/s 1027.61038.6

20

R

ua

down)y (verticallm/s 1092.220)1029.7(22235

uaC

PPA

2π·sinφ

Coriolis force elsewhereFoucault pendulum, Paris: φ = 48.8°

What is the local angular speed?

sin

vaC

sin2

φ

φ

A

P

Paris

http://enggar.net/page/12/?s/

3.11rad197.036001049.55

t

In Paris: φ = 48.8°

One period of the Panthéon pendulum is 16.4 sec.

(a) How much does it turn in an hour?

(b) Displacement between two successive swings

on a circle of radius 3 m?

rad1001.94.161049.545

t

mm7.231001.94

rt

s/1049.58.48sin1029.7sin55

r = 2 cm, v = 10 cm/s

(a) Find the acceleration towards

the centre.

(b) What is the contribution of the

Coriolis force to this?

2

22

m/s 5.002.0

1.0

r

va

sin2 vaC

255m/s1015.47sin)103.7(1.02

Is the Coriolis force important?

No

Find (a) radius of spot

1° corresponds to

≈ 9° means r ≈ 1.1·107 m

(b) acceleration of gas

(c) Coriolis acceleration

m102.1360

104.1

360

2 68

R

Jupiter: T = 9.8 hours,

R = 71 900 km (equatorial)

Great Red Spot φ = 22° (S),

wind v ≈ 100 m/s

2

4

s

m109

a

2

4

Cs

m103.1

a Ye

s

www.celestiamotherlode.net/catalog/jupiter.php

http://www.japantimes.co.jp/news/2014/06/18/national/shinkansen-tops-list-100-innovative-postwar-technologies/#.Va84VPkmHpE

Shinkansen train v = 200 km/h

Tokyo to Osaka, both N55°

35sin103.76.3

2002sin2

5va

C

g0005.0s

m0047.0

2

No

Golfer in Scotland (N55°)

can hit the ball to 300 m at 45° angle.

What is the deviation of the ball

owing to the Coriolis force?

g

vt

sin20

g

v

g

vv

cossin2sin2cos

2

000

m3008.98.9

2

1

2

12 2

0

2

0

v

v

,s

m548.9300

0v st 7.8

8.9

45sin542

cossin2 0C va

2

5

s

m0046.045cos5455sin103.72

cm177.80046.02

1

2

1 22

C tad No

Artillery missile, N50°,

v0 = 700 m/s towards the East, at 45° angle.

Deviation owing to the Coriolis force?

g

v

g

vv

cossin2sin2cosRange

2

00

0km50

8.9

2

1

2

17002

2

2

00

2

C

sin2)cossin2(

2

1

2

1

g

vvtad

cossin

sin4 23

02v

g

m28045cos45sin7008.9

50sin103.74 23

2

5

Ye

s

Frictionless and horizontal ice rink, 30 m wide,

Puck given an initial velocity.

Coriolis force only: circular motion

Find:

(a) speed needed in Budapest (N47.5°)

Note:

(b) What is the radius if the speed is 1 m/s?

At 10° latitude? At 80°?

vr

v sin2

2

local2sin2

r

v

s

mm61.0155.47sin103.72sin2

5

rv

km) 7.0 km, (39 km3.95.47sin103.72

1

sin25

vr

An interesting kind of motion

Buoy in the Baltic Sea,

SE of Stockholm, N57°

Design a space station:

• Cylindrical shape

• Artificial gravity is provided

by centrifugal force owing to

spinning about the axis.

• Coriolis force on crew walking

at 1 m/s is no greater than

0.05mg .

gr 2

2s

m1005.0

s

m12

s

125.0

m16025.0

10

22

gr

http://www.astronautix.com/craft/span1984.htm

Both forces to consider

References

Anders O. Persson The Coriolis Effect: Four centuries of conflict between common sense and mathematics, History of Meteorology 2 (2005)

THE END

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