1. Reporter: Julian Ronacher
No. 13 Spinning Ice
Pour very hot water into a cup and stir it so the water rotates slowly. Place a small ice cube at the centre of the rotating water. The ice cube will spin faster than the water around it. Investigate the parameters that influence the ice rotation.
Team Austria
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2. Overview Experiment Experimental setup Observations and measurements
Basic theory
Conservation of momentum
Mathematical theory
Expanded experiments
Special case
Combination of theory with the experiments
References
Team of Austria – Problem no. 13 – Spinning Ice

3. First experiments
Team of Austria – Problem no. 13 – Spinning Ice

4. First experiments
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5. Basic theory Ice cube begins to spin Water rotation
Ice cube begins to melt
High water temperature
Tornado effect
Conservation of momentum
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6. Basic theory Tornado effect Cold water is flowing down to the ground
Spinning round
Water from the side of the ice cube has to fill the gap
Ice cube gets accelerated
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7. Basic theory
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8. Basic theory
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9. Basic theory Conservation of momentum
Mass and radius of the ice cube decrease
Angular velocity increases
M = torsional moment
L = angular momentum
Θ = moment of inertia
ω = angular velocity
M = torsional moment
L = angular momentum
Θ = moment of inertia
ω = angular velocity
m = mass of the ice cube
ρ = density of the ice cube
h = height of the ice cube
m = mass of the ice cube
ρ = density of the ice cube
h = height of the ice cube
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10. Mathematic theory h = constant
Ice cube is completely covered with water
Q = heat energy
Qhf = heat of fusion
t = time
α = heat transmission coefficient
R = radius of the ice cube
h = height of the ice cube
T = temperature
m = mass of the ice cube
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11. Mathematic theory ρ = density m = mass V = volume R = radius
h = height
α = heat transmission coefficient
T = temperature
Q = heat of fusion
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12. Mathematic theory M = torsional momentum η = viscosity of water
ω = angular velocity
δ = boundary layer thickness
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13. => Mathematic theory m = mass ω = angular velocity h = height
η = viscosity
δ = boundary layer thickness
ρ = density
α = heat transmission coefficient
T = temperature
Qhf = heat of fusion
t = time
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14. Mathematic theory ω = angular velocity of the tornado
Γ = circulation in the flowing fluid
r = radius of the tornado at a specific height
p = pressure
ρ = density
g = acceleration
z = height of the ice cube
A = value of p at r = ∞ and z = h
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15. Mathematic theory ω = angular velocity of the tornado
Γ = circulation in the flowing fluid
r = radius of the tornado at a specific height
p = pressure
ρ = density
g = acceleration
z = height of the ice cube
A = value of p at r = ∞ and z = h
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16. Expanded experiments Special case
Angular velocity of the ice cube and the water are the same
No relative movement between ice cube and water
Although the ice cube becomes faster than the water
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17. Expanded experiments Team of Austria – Problem no. 13 – Spinning Ice17

18. Expanded experiments Team of Austria – Problem no. 13 – Spinning Ice18

19. Expanded experiments Water accelerates the ice cube viscosity
Ice cube still independent from the water
No tornado effect
Ice cube can become faster
By loss of mass and radius
Tornado effect again
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20. Combination of theory with the experiments
Tornado effect
Angular velocity of the ice cube: 2,05 1/sec
Conservation of momentum
Angular velocity of the ice cube: 0,73 1/sec
All together: 2,78 1/sec
Experiments
Angular velocity of the ice cube: 2,9 1/sec
Measurement error: 5%
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21. References
Taschenbuch der Physik; Stöcker; Verlag Harri Deutsch; 5. Auflage
Mathematik für Physiker; Helmut Fischer; Teubner Verlag; 5. Auflage
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22. Extra Slides Mathematical background
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23. Mathematical background
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24. Mathematical background
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25. Mathematical background
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26. Mathematical background
water
ice cube δ ω F
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27. Mathematical background
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28. Mathematical background
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