Theory Experiment Conclusion

12 - Levitating spinner

Team Talnet

TALNET o. s.http://www.talnet.cz

with the support of

Faculty of Mathematics and Physics – Charles University in Praguehttp://www.mff.cuni.cz

April 14, 2011

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion

Assigment

Levitating spinner

A toy consists of a magnetic spinning top and a plate containing magnets(e.g. ”Levitron”). The top may levitate above the magnetic plate. Underwhat conditions can one observe the phenomenon?

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion

Content

1 Theory

2 ExperimentLevitatingFrequencyMagnetic field

3 Conclusion

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion

Equilibrium position

Toroid magnet

Fmag . . . magnetic force

FG . . . gravitational force

Net force is zeroFG + Fmag = 0

Figure: Two magnets

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion

Conditions for stability

Ep

xm× B =M

m . . . magnetic dipole moment of a spinnerB . . . magnetic field of levitronM . . . moment of force

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion

Conditions for stability

Gyroscopic efect

L

FG

−FG

M

M = dLdt

M . . . moment of forceL . . . angular momentumt . . . time

Change of angular momentum moves it towards moment of force

Axis begins rotating

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion

Precession

Angular velocity of precession ωp

ωp =MIs ωs

ωs – angular velocity of spin about the spin axisM – moment of forceIs – moment of inertia

ωp, ωs – inversly proportional

ωp too high → rotation about horizontal axis → levitron falls

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion Levitating Frequency Magnetic field

Video

2 minutes

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion Levitating Frequency Magnetic field

Frequency

Stroboscopic camera (600 fps)→ video

Measured: 20 – 31 rps

Stated by producer: 18 – 40 rps

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion Levitating Frequency Magnetic field

Magnetic field

Magnetic field orientation

0

2

4

6

8

10

-8 -6 -4 -2 0 2 4 6 8

[cm

]

[cm]

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion Levitating Frequency Magnetic field

Magnetic field

Magnetic field sensor, low range

Dependence of vertical component of magnetic field intensity vectoron height above levitron

0 2

4 6

8 10

-0.5-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5

-8-6-4-2 0 2 4 6

B [mT]

h [cm]

D/D0

B [mT]

-8-6-4-2 0 2 4 6

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion Levitating Frequency Magnetic field

Comparison

0 2

4 6

8 10

-0.5-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5

-8-6-4-2 0 2 4 6

B [mT]

h [cm]

D/D0

B [mT]

-8-6-4-2 0 2 4 6

0

2

4

6

8

10

-8 -6 -4 -2 0 2 4 6 8

[cm

]

[cm]

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion

Conclusion

Equilibrium positionFG + Fmag = 0Stability

M . . . moment offorceM = dL

dt

ExperimentsFrequencyMagnetic fieldintensity

0 2

4 6

8 10

-0.5-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5

-8-6-4-2 0 2 4 6

B [mT]

h [cm]

D/D0

B [mT]

-8-6-4-2 0 2 4 6

Team Talnet 12 - Levitating spinner

Theory Experiment Conclusion

Thank you for your attention

Team Talnet 12 - Levitating spinner