A111 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.

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