Rolling Motion

A uniform solid sphere is given velocity $v_0$ and angular velocity ${\omega }_0= \frac{v_0}{2R}$ and placed on a rough horizontal surface as shown. The velocity of centre of mass when pure rolling starts, is

A disc of radius $0.1\mathrm{ }\mathrm{m}$ rolls without sliding on a horizontal surface with a velocity of $6\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ . It then ascends a smooth continuous track as shown in figure. The height upto which it will ascend is (in $\mathrm{cm}$) : ( $g=10\mathrm{ }{\mathrm{m} \mathrm{s}}^{-2}$ )

From a triangular lamina of side a and mass $m$ , a small triangular Lamina made by joining mid-points of sides of triangular lamina is cut. If Moment of Inertia of complete Lamina about COM is $I_o$ and Moment of Inertia of remaining Lamina about centroid is $\frac{x{I}_0}{16}$, then find the value of $x$.

What is the moment of inertia for a disk?

What is transverse moment of inertia?

What is the moment of inertia of a cylinder about its axis?

What is the moment of inertia of solid cylinder with the axis passing through its centre?
 

How do you find the moment of inertia of a thin ring?

What is the formula of theorem of perpendicular axis?

What is moment of inertia of disc?

What is moment of inertia of a ring?

What is the formula of moment of inertia for circle?

What is moment of inertia of a ring about a tangent parallel to plane of ring?

What is the moment of inertia of a ring about a tangent?

What is the moment of inertia of solid cylinder with the axis passing through its centre?

What is moment of inertia of ring about tangent?

What is the moment of inertia of semicircular ring?

The moment of inertia of a hollow cubical box of mass $M$ and side length $a$, about an axis passing through centres of two opposite faces, is equal to $\frac{xM{a}^2}{18}$. The value of $x$ is

Let $I_1$ and $I_2$ be the moments of inertia of two bodies of identical geometrical shape, the first made of aluminium and the second of iron. Then, which of the following statements is true?

A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, what happens to the moment of inertia of water about the axis?