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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

powered by:

Experimental setup

Observations and measurements

Basic theory

Conservation of momentum

Mathematical theory

Expanded experiments

Special case

Combination of theory with the experiments

References

OverviewTeam of Austria – Problem no. 13 – Spinning Ice

First experiments

Team of Austria – Problem no. 13 – Spinning Ice

Basic theory

Ice cube begins to spin

Water rotation

Ice cube begins to melt

High water temperature

Tornado effect

Conservation of momentum

Team of Austria – Problem no. 13 – Spinning Ice

5

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

Team of Austria – Problem no. 13 – Spinning Ice

6

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

Team of Austria – Problem no. 13 – Spinning Ice

9

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

Team of Austria – Problem no. 13 – Spinning Ice

10

Mathematic theory

ρ = density

m = mass

V = volume

R = radius

h = height

α = heat transmission coefficient

T = temperature

Q = heat of fusion

Team of Austria – Problem no. 13 – Spinning Ice

11

Mathematic theory

M = torsional momentum

η = viscosity of water

ω = angular velocity

δ = boundary layer thickness

Team of Austria – Problem no. 13 – Spinning Ice

12

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

Team of Austria – Problem no. 13 – Spinning Ice

13

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

Team of Austria – Problem no. 13 – Spinning Ice

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

Team of Austria – Problem no. 13 – Spinning Ice

15

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

Team of Austria – Problem no. 13 – Spinning Ice

16

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

Team of Austria – Problem no. 13 – Spinning Ice

19

Combination of theory with the experiments

Theory

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%

±

Team of Austria – Problem no. 13 – Spinning Ice

20

References

Taschenbuch der Physik; Stöcker; Verlag Harri Deutsch; 5. Auflage

Mathematik für Physiker; Helmut Fischer; Teubner Verlag; 5. Auflage

Team of Austria – Problem no. 13 – Spinning Ice

21

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