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Chapter 1: Q28 E (page 1)

Four small spheres, each of which you can regard as a point of mass of 0.200 kg, are arranged in a square of 0.400 m on a side and connected by extremely light rods (Fig. E9.28). Find the moment of inertia of the system about an axis

through the center of the square, perpendicular to its plane (an axis through point O in the figure);

bisecting two opposite sides of the square (an axis along the line AB in the figure);

that passes through the centers of the upper left and lower right spheres and point O.

Short Answer

Expert verified

(a) the center of the square, perpendicular to its plane is 0.0640km.m2

(b) Bisecting two opposite sides of the square is 0.032kg.m2.

(c) The center of the upper left and lower right sphere and through point o is 0.0320kg.m2

Step by step solution

01

Step:-1 explanation

If we want to solve our question. we will be applying an equation that determines the moment of inertia

I=∑miri2

Where, a Imoment of the inertia

mi=mass

ri= distance from the axis of the rotation.

Step:-2 Concept

The center of the square, perpendicular to its plane

Here, we will assume applying the Pythagorean theorem,

First, we will calculate the distance from the axis.

____________(1)

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