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Consider a merry-go-round that has the form of a disc with radius 5.5 m and mass 155 kg. If five children, each of mass 20 kg, sit on the outer edge of the merry-go-round, what is the total moment of inertia?

Respuesta :

Answer:

[tex]I=5369.375[/tex]

Explanation:

Given:

  • mass of merry go round, [tex]M=155\ kg[/tex]
  • radius of merry go round, [tex]r=5.5\ m[/tex]
  • mass of child, [tex]m=20\ kg[/tex]

Considering merry-go-round as a disk, its moment of inertia is given as:

[tex]I_d=\frac{1}{2} M.r^2[/tex]

[tex]I_d=0.5\times 155\times 5.5^2[/tex]

[tex]I_d=2344.375\ kg.m^2[/tex]

Considering children as point masses, their moment of inertia is given as:

[tex]I_C=5(m.r^2)[/tex]

since there are 5 children

[tex]I_C=5\times20\times 5.5^2[/tex]

[tex]I_C=3025\ kg.m^2[/tex]

Now, total moment of inertia:

[tex]I=I_C+I_d[/tex]

[tex]I=3025+2344.375[/tex]

[tex]I=5369.375[/tex]

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