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A 103 kg horizontal platform is a uniform disk of radius 1.71 m and can rotate about the vertical axis through its center. A 68.9 kg person stands on the platform at a distance of 1.09 m from the center, and a 27.7 kg dog sits on the platform near the person 1.45 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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Answer:


I_(total)=220.64 kg*m^(2)

Step-by-step explanation:

The moment of inertia of the system is equal to the each population and the platform inertia so

Inertia disk


I_(disk)=(1)/(2)*m_(disk)*(r_(p))^(2)

Inertia person


I_(p)=(1)/(2)*m_(p)*(r_(p))^(2)

Inertia dog


I_(d)=(1)/(2)*m_(d)*(r_(d))^(2)

The Inertia of the system is the sum of each mass taking into account that all exert the force of inertia:


I_(total)=I_(disk)+I_(p)+I_(d)


I_(total)=(1)/(2)*103kg*(1.71)^(2)+(1)/(2)*68.9kg*(1.09)^(2)+(1)/(2)*27.7kg*(1.45)^(2)


I_(total)=220.64 kg*m^(2)

User Dominic Brunetti
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