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 powered by: 1

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

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

First experiments Team of Austria – Problem no. 13 – Spinning Ice 4

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 Team of Austria – Problem no. 13 – Spinning Ice 7

Basic theory Team of Austria – Problem no. 13 – Spinning Ice 8

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 Team of Austria – Problem no. 13 – Spinning Ice 17

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

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 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

Extra Slides Mathematical background Team of Austria – Problem no. 13 – Spinning Ice 22

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Mathematical background water ice cube δ ω F => Team of Austria – Problem no. 13 – Spinning Ice 26

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Mathematical background Team of Austria – Problem no. 13 – Spinning Ice 28