A 111 kg horizontal platform is a uniform disk of radius 1.73 m and can rotate about the vertical axis through its center. A 66.9 kg person stands on the platform at a distance of 1.17m from the center, and a 25.3 kg dog sits on the platform near the person 1.35 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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The moment of inertia of this system is 303.89 kg * m²

Explanation:

Step 1: Data given

mass of the disk = 111 kg

radius of the disk = 1.73 m ⇒ formule will be I = 1/2 MR²

mass of the person = 66.9 kg

distance form the center = 1.17m

mass of the dog = 25.3 kg

distance from the centrer 1.35m

Step 2: Calculate moment of inertia

I = ∑Mi * (Ri) ²

I = I (disk) + I (person) + I (dog)

Step 3: Calculate moment of inertia of the disk

I = (1/2) MR² = (1/2) * 111*1.73²

I = 166.2

Step 4: Calculate moment of inertia of the person

I = MR² = 66.9*1.17²

I = 91.58

Step 5: Calculate moment of inertia of the dog

I = MR² = 25.3*1.35²

I = 46.11

Step 6 : Calculate moment of inertia

I = ∑I = 166.2 + 91.58 + 46.11 = 303.89 kg * m²

The moment of inertia of this system is 303.89 kg * m²