Swirling Disc in Chocolate!

Classical Mechanics Level 4

Find the External Torque that has to be supplied to a disc rotating about an axis perpendicular to it and passing through its center of mass to maintain it at the same angular velocity, placed on top of a layer of viscous liquid of coefficient of viscosity \(\eta\) of height \(h\). Give your answer to 2 decimal places.

It is a thin disc. The brown liquid is the viscous liquid.

Details and Assumptions:

  • Mass of Disc : \(M = 1 \text{ kg}\)

  • Radius of Disc : \(r = 2 \text{ m}\)

  • Height of Liquid layer : \(h = 0.15 \text{ m}\)

  • Coefficient of Viscosity : \(\eta = 20 \text{ S.I Units}\)

  • Initial angular velocity : \(\omega = \frac {10}{\pi} \text{ rad/s}\)

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