Question

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.

Answer 1

I = 274.75 kg-m²

Step-by-step 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 =
`(1)/(2)MR^2`

Moment of inertia of the system

`I = MOI\ of\ disk + m_p r_p^2 + m_d r_d^2`

`I = (1)/(2)MR^2 + m_p r_p^2 + m_d r_d^2`

`I = (1)/(2)* 129 * 1.51^2 + 67.5 * 1.09^2 + 25.3* 1.37^2`

I = 274.75 kg-m²