Rotational Motion

From a uniform circular disc of mass M and R, part AOC is removed as shown in the figure. The M.I. of the remaining portion of the disc about an axis passing through the centre and perpendicular to the plane of the disc…

Four point masses each of mass m, are arranged in X-Y plane as shown in the figure The moment of intertia of this system about X - axis is

A mass m supported by massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release? $\{g$ =…

A very thin, uniform disc is made by removing a small disc of diameter $2R$ from a bigger (thin, uniform) disc of uniform mass density, mass $M$, and radius $2R$, as shown in the figure. The M.I. of this remaining part…

The moment of inertia of a uniform circular disc rotating about an axis perpendicular to the plane of the disc and passing through points O, A, B and C are $I_o$, $I_A$, $I_B$ and $I_C$ respectively, then

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $\omega$. Six objects, each of mass m, are kept gently to the opposite ends of three diameters of the ring. The…

A disc has mass 'M' and radius 'R'. The axis of rotation passes through a point P in the plane of the disc, which is at a distance 'x' $(x < R)$ from the center of the disc and perpendicular to the plane of the disc.…

Moment of inertia of a disc about its own axis is I. Its moment of inertia about a tangential axis in its plane is

A stone of mass $m$, tied to the end of a string, is whirled around in a horizontal circle. The length of the string is reduced gradually, keeping the angular momentum of the stone about the centre of the circle…

A solid disc of radius $40\ \text{cm}$ and the mass of $20\ \text{kg}$ is rotating with an angular velocity of $300\ \text{rpm}$, about an axis passing through its centre of mass and perpendicular to its plane. The…

If $\vec{r}$ is a position vector of the body and $\vec{p}$ is linear momentum, $\vec{r}=2\hat{i}+3\hat{j}-3\hat{k}$ and $\vec{p}=2\hat{i}+4\hat{j}-5\hat{k}$. The angular momentum of the body is

The radius of gyration of a thin hollow cylinder of radius $R$ about a tangential axis passing perpendicular to the plane of the cylinder and parallel to the geometrical axis is