Question

Axis of Rotation and Moment of Inertia Ranking Task 

Two identical uniform solid spheres are attached by a solid uniform thin rod, as shown in (Figure 1). The rod lies on a line connecting the centers of mass of the two spheres. The axes A, B, C, and D are in the plane of the page (which also contains the centers of mass of the spheres and the rod), while axes E and F (represented by black dots) are perpendicular to the page.

Part A

Rank the moments of inertia of this object about the axes indicated.

Answer 1

Answer 2

Correct order is:

(C and F), B, (A and E), D

Moments of inertia, I = Δm r²

• Axes C and F would represent the largest moments of inertia because the center of mass of the rotating body is furthest from these two axes of rotation. However, C and F would have equal moments of inertia because they have equal distance from the center of mass to their respective axis of rotation.
• 2nd largest would be B because it is the next closest distance from the center of mass.
• Next would be A and E, because although they are exactly between the two rotating masses.
• D has the lowest moment of inertia because the perpendicular distance from the axis of rotation never exceeds the radius of one of the balls.

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