Calculate the moment of inertia of the system shown in the figure about the axis of rotation $XX'$.

If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his

Two point masses of $0.3 \ kg$ and $0.7 \ kg$ are fixed at the ends of a rod of length $1.4 \ m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

What is the moment of inertia of a cylinder of diameter $D$ and length $L$ about an axis passing through its center of gravity and perpendicular to its length?

Four particles of masses $5 \ kg, 2 \ kg, 3 \ kg$,and $4 \ kg$ are placed at $(0, 0, 0), (2, 0, 0), (0, 3, 0)$,and $(-2, -2, 0)$ respectively. The moments of inertia about the $x$-axis,$y$-axis,and $z$-axis respectively are:

What is analogous to mass in linear motion for rotational motion?