A ring of mass \( M = 3 \text{ kg}\) and radius \( R = 3 \text{ m}\) rotates about its center. If three identical balls each of mass \( m = 6 \text{ kg} \) are attached on the ring, what is the total moment of inertia of the ring and balls?

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A solid sphere of mass \( M = 15 \text{ kg}\) with homogeneous density rotates about its center. If the sphere's radius is \(R=5\text{ m},\) what is its moment of inertia?

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A solid cylinder of mass \( M = 8 \text{ kg}\) with homogeneous density has a circular base of radius \( R = 5 \text{ m}\) and a height of \( H = 5 \text{ m}.\) If the cylinder rotates about its center, as illustrated in the above diagram, what is its moment of inertia?

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