Question

Four small spheres, each of which can be regarded as a point mass of 0.200 kg, are arranged in a square 0.400 m and connected by extremely light rods. Find the moment of inertia of the system about an axis

a) through the center of the square O, perpendicular to the plane of the square

b) bisecting two opposite sides of the square (line A-B in the figure)

c) passing through O along a diagonal of the square

d) Suppose the masses of the rods are not negligible but also equal to 0.200 kg each. Repeat your calculation in part a) to c)

 (Hint: For a flat object that lies entirely within a plane, the moments of inertia about the x, y and z axis are related by , where all axes go through the same point and the z axis is perpendicular to the plane of the object (perpendicular axis theorem)).

Answer 1

[REMOVED]

Answer 2

a.
Required moment of inertia
= 4 * (0.200) * (0.200 * v2)² kgm²= 0.064 kgm²

b.
Required moment of inertia
= (1/2) * (0.64) = 0.032 kgm²

c.
The moment of inertia of the spheres lying on the axis is zero.
The sum of the moments of inertia of the remaining two spheres
= 2 * (0.200) * (0.200 * v2)²= 0.032 kgm².