Question #108070

Four objects are held in position at the corners of a rectangle by light rods as shown in Figure P8.37. Find the moment of iner- tia of the system about (a)thex-axis,(b)they-axis, and (c) an axis through O and perpendicular to the page

Expert's answer

**Solution**

The moment of inertia of a mass *m* placed *r* meters from the axis of rotation is

This is is an additive quantity. Therefore, the moment of inertia around x-axis will be

where

"I_x=m_1r_1^2+m_2r^2_2+m_3r^2_3+m_4r^2_4,\\\\r_1=r_2=r_3=r_4=3\\text{ m}.\\\\\nI_x=(3.1+1.7+4.5+2.3)3^2=104\\text{ kg}\\cdot\\text{m}^2."Consider rotation around y-axis:

Now consider rotation around z-axis:

Conclusion: the further, the higher.

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