A 129-kg horizontal platform is a uniform disk of radius 1.51 m and can rotate about the vertical axis through its center. A 67.5-kg person stands on the platform at a distance of 1.09 m from the center and a 25.3-kg dog sits on the platform near the person, 1.37 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.

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wagonbelleville wagonbelleville · Answer 1 · 2019-12-03T10:08:10+01:00

Answer:

I = 274.75 kg-m²

Explanation:

given,

mass of horizontal platform = 129 Kg

radius of the disk = 1.51 m

mass of the person(m_p) = 67.5 Kg

standing at distance(r_p) = 1.09 m

mass of dog(m_d) = 25.3 Kg

sitting near the person(r_d) = 1.37 m from center

moment of inertia = ?

Moment of inertia of disc = [tex]\dfrac{1}{2}MR^2[/tex]

Moment of inertia of the system

[tex]I = MOI\ of\ disk + m_p r_p^2 + m_d r_d^2[/tex]

[tex]I = \dfrac{1}{2}MR^2 + m_p r_p^2 + m_d r_d^2[/tex]

[tex]I = \dfrac{1}{2}\times 129 \times 1.51^2 + 67.5 \times 1.09^2 + 25.3\times 1.37^2[/tex]

I = 274.75 kg-m²