Rotational Motion

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…

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

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…

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? $\{g$ =…

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

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

A thin rod of mass '$m$' and length '$2l$' is made to rotate about an axis passing through its center and perpendicular to its length. If the angular velocity changes from $0$ to $\omega$ in time '$t$', then the torque…

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…

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 uniform disc of mass '$m$' and radius '$R$' is rolling up a rough inclined plane which makes an angle of $30^\circ$ with the horizontal. If the coefficient of friction is $\mu$ and only forces acting are gravitational…

A solid, homogeneous sphere of mass M and radius R is rolling down a rough inclined plane inclined at an angle $\theta$. Which of the following statements is INCORRECT?

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