Rotational Motion

Four particles, each of mass $1\mathrm{kg}$are placed at four corners of a square ofside $2m$. The moment of inertia of thesystem about an axis perpendicular to its plane and passing through one of its vertex is…

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the…

Two identical spheres each of mass $2\mathrm{kg}$and radius $50\mathrm{cm}$are fixed at the ends of a light rod so that the separation between the centers is $150\mathrm{cm}$. Then, moment of inertia of the system about…

Moment of inertia about an axis $AB$ for a rod of mass $40$ kg and length $3$ m is same as that of a solid sphere of mass of $10$ kg and radius $R$ about an axis parallel to $AB$ axis with separation of $3$ m as shown…

A body of mass $m$is projected with a speed $u$making an angle of $45^{o}$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed…

$I_{\mathrm{CM}}$ is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. $I_{\mathrm{AB}}$ is its moment of inertia about an axis ABperpendicular to…

Three balls of masses $2 \mathrm{~kg}, 4 \mathrm{~kg}$ and $6 \mathrm{~kg}$ respectively are arranged at centre of the edges of an equilateral triangle of side $2 \mathrm{~m}$. The moment of intertia of the system about…

A heavy iron bar of weight $12\mathrm{kg}$ is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle $60^{\circ}$ with the horizontal, the normal forceappliedby the man on baris:

Suppose there is a uniform circular disc of mass $M \mathrm{~kg}$ and radius $r \mathrm{~m}$ shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis $A$ of…

A cylinder is rolling down on an inclined plane of inclination $60^{\circ}$. Its acceleration during rolling down will be $\frac{x}{\sqrt{3}}ms^{-2}$, where $x=$_______(use $g=10ms^{-2}$)?

A uniform disc of mass $0.5\mathrm{kg}$ and radius $r$ is projected with velocity $18ms^{-1}$ at $t=0s$ on a rough horizontal surface. It starts off with a purely sliding motion at $t=0s$. After $2s$ it acquires a…

Two iron solid discs of negligible thickness have radii $R_1$ and $R_2$ and moment of intertia $I_1$ and $I_2$, respectively. For $R_2=2 R_1$, the ratio of $I_1$ and $I_2$ would be $1 / x$, where $\mathrm{x}=$ ________ -