Torque and Rotational Motion

A particle of mass $m$ is rotating at a distance $r$ from the axis of rotation. What is its rotational inertia?

A thin rod of mass $M$ and length $L$ is rotated about an axis perpendicular to the rod. To calculate the rotational inertia using integration, which integral would you use?

A thin rod has a rotational inertia of $I_{cm}$ about its center of mass. What is the rotational inertia about a parallel axis a distance $d$ away from the center of mass, if the rod has a mass $M$?

A thin rod of length $L$ and mass $M$ has a non-uniform density. To find the rotational inertia about one end, which method would you use?

Which of the following best describes rotational inertia?

Three objects with masses $m_1$, $m_2$, and $m_3$ are located at distances $r_1$, $r_2$, and $r_3$ from the axis of rotation, respectively. What is the total rotational inertia of the system?

A solid sphere and a hollow sphere have the same mass and radius. Which one has a larger rotational inertia about an axis through its center?

About which axis of rotation is the rotational inertia of a rigid body the smallest?

A complex object has a rotational inertia $I_{cm}$ about its center of mass. Calculating the rotational inertia about an axis that is not through the center of mass would be best solved by which method?

A thin rod of mass $M$ and length $L$ has a rotational inertia of $\frac{1}{12}ML^2$ about its center of mass. First, calculate the rotational inertia about the center of mass using integration. Second, apply the parallel axis theorem to find the rotational inertia about an axis at one end.