Question

Four masses are at corners of a rectangle connected by massless rods as shown in Figure 0.27.
(i) What is the moment of inertia of the system when the axis of rotation is along the x-axis?

(ii) What is the moment of inertia of the system when the axis of rotation is along the y-axis?
(iIi) What is the moment of inertia of the system when the axis of rotation goes through point O and is perpendicular to the xy-plane.

4.0kg 3.0kg 6m 6.0kg1.0kg 1.0kg 4m

Answer 1

apply from the formula of moment of inertia I = mr^2

for the system shown here

apply accordingly

moment of inertia of a point mass about an axis = m R^2

about x axis, I = 4 *3^2 + 3 *3^2 + 6 * 3^2 + 1 * 3^2

I = = 126 kg m^2

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B) about y, I = 4 *2^2 + 3 *2^2 + 6 *2^2 + 1*2^2

I = 56 kg m^2

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C) Using perpendicular axis theorem, Ixy = Ix + Iy

Ixy = 126 + 56 = 182 kg m^2