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The sculpture in the diagram above has four identical beads that are spread at even intervals across a solid $3.0\text{ m}$ pipe. The beads are solid, with uniform density. They each have a radius of $16\text{ cm}$ and a mass of $5\text{ kg}$; the pipe has a mass of $20.0\text{ kg}$. The pipe reaches from the center of the left-most bead to the center of the right-most bead.

Rotational Inertia Equations

Shape Axis Rotational Inertia
Solid Sphere Center $I=\cfrac{2}{5}\text { } mr^2$
Solid Rod Center; perpendicular to length $I = \cfrac{1}{12}\text{ }mL^2$
Solid Rod End; perpendicular to length $I=\cfrac{1}{3}\text{ }mL^2$
Point Mass $I =mr^2$

Determine the rotational inertia of the sculpture, about an axis of rotation perpendicular to the sculpture, running through the middle, as shown by the dotted line in the diagram.

A

$I = 33 \text{ kg} \cdot \text{m}^2$

B

$I = 40 \text{ kg} \cdot \text{m}^2$

C

$I = 51 \text{ kg} \cdot \text{m}^2$

D

$I = 62 \text{ kg} \cdot \text{m}^2$

E

$I = 85 \text{ kg} \cdot \text{m}^2$

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