A side view of three turntables is shown in the figure below. The curly arrow shows the direction of rotation. Turntable (i) is a disk of mass \(10\) \(\rm{kg}\) and supports a \(5\) \(\rm{kg}\) mass at each end as seen in the figure. Turntable (ii) is a disk of mass \(10\) \(\rm{kg}\) and supports two masses of \(5\) \(\rm{kg}\) each near its centre. Turntable (iii) is massless and supports \(10\) \(\rm{kg}\) of mass at each end.

Part 1#

Rank the moments of inertia:

The figure is as described in the question and the arrows are counter clockwise.

Answer Section#

  • \(I_{i}\) > \(I_{ii}\) > \(I_{iii}\)

  • \(I_{iii}\) > \(I_{ii}\) > \(I_{i}\)

  • \(I_{iii}\) > \(I_{i}\) > \(I_{ii}\)

  • \(I_{ii}\) > \(I_{i}\) > \(I_{iii}\)

  • All three have the same moment of inertia since they have the same total mass.


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