Question

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.

Answer 1

Answer:

$I_{total}=220.64 kg*m^{2}$

Explanation:

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

Inertia disk

$I_{disk}=\frac{1}{2}*m_{disk}*(r_{p})^{2}$

Inertia person

$I_{p}=\frac{1}{2}*m_{p}*(r_{p})^{2}$

Inertia dog

$I_{d}=\frac{1}{2}*m_{d}*(r_{d})^{2}$

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

$I_{total}=I_{disk}+I_{p}+I_{d}$

$I_{total}=\frac{1}{2}*103kg*(1.71)^{2}+\frac{1}{2}*68.9kg*(1.09)^{2}+\frac{1}{2}*27.7kg*(1.45)^{2}$

$I_{total}=220.64 kg*m^{2}$