Moment of Inertia

Four point masses $($each of mass $m$$)$ are arranged in the $X-Y$ plane. The moment of inertia of this array of masses about $Y$-axis is 

What is moment of inertia? List the factors on which it depends. 

A body of mass $800 \mathrm{kg}$ is rotating about an axis. The distance of the centre of mass of the body from the axis of rotation is $200 \mathrm{cm}$. Find the moment of inertia of the body about the axis of rotation.

What is the importance of moment of inertia?

The moment of inertia of an annular disc of mass M, outer and inner radii R and r, about its diameter is :

The spokes used in a cycle wheel increase its

M.O.I is the ratio of 

A solid sphere, a thin ring and a cylinder of same mass and radius, held at rest are released simultaneously to roll down on an inclined plane. Which one will reach the bottom first?

Point masses $1, 2, 3$ and $4 \mathrm{kg}$ are lying at the points $(0, 0, 0), (2, 0, 0), (0, 3, 0)$ and $(-2, -2, 0)$, respectively. The moment of inertia of this system about the $x$-axis will be,

Four similar point masses (each of mass $m$) are placed on the circumference of a disk of mass $M$ and radius $R$. The moment of inertia of the system about the normal axis through the center $O$ will be,

On the marks of $20 \mathrm{cm}$ and $70 \mathrm{cm}$ of a light meter scale, two weights, $1 \mathrm{kg}$ and $4 \mathrm{kg}$, respectively, are placed. The moment of inertia (in $\mathrm{kg} {\mathrm{m}}^2$) about the vertical axis through the $100 \mathrm{cm}$ mark will be,

M.O.I is the ratio of 

M.O.I. of a disc is minimum about an axis 

A pulley of radius $2 \mathrm{m}$ is rotated about its axis by a force $F=\left(20t-5t^2\right)$ Newton (where, $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10 {\mathrm{kgm}}^2,$ the number of rotations made by the pulley before its direction of motion is reversed, is

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is

Moment of inertia is the rotational analogue of 

Name the quantity, in linear motion, which is equivalent to moment of inertia in rotational motion.

When a ceiling fan is switched off, its angular velocity reduces to $50\%$ while it makes $36$ rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)

The moment of inertia of two spheres of equal masses about their diameters is equal. If one of them is solid and other is hollow, the ratio of their radii is

Three identical thin rods each of length $l$ and mass $M$ are joined together to form a letter $H$. What is the moment of inertia of the system about one of the sides of $H$?