Rotational Motion

A light rod of length,$l$ has two masses,$m_{1}$ and $m_{2}$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centreof mass is

A solid sphere $A$ of radius $R$ and mass $M$ is attached at a point to a smaller solid sphere $B$ of radius $r < R$ and mass $m < M$. Assume that the line joining their centres lies along the horizontal. The moment of…

From a disc of radius $R$ and mass $M$, a circular hole of diameter $R$, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing…

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through

A small mass attached to a string rotates on frictionless table top as shown. If the tension is the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2 , the…

Three identical spherical shells, each of mass $m$and radius $r$are placed as shown in the figure. Consider an axis $XX^{'}$ which is touching the two shells and passing through the diameter of the third shell. The…

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

Two rotating bodies,$A$ and $B$ of masses,$m$ and $2m$ with moments of inertia. $I_{A}$ and $I_{B}\left(I_{B}>I_{A}\right)$ have equal kinetic energyof rotation. If,$L_{A}$ and $L_{B}$ be their angular momenta,…

The ratio of the acceleration for a solid sphere (mass $'m'$ and radius $R)$ rolling down an incline of angle $'\theta\,'$ without slipping and slipping down the incline without rolling is:

A uniform circular disc of radius 50 cm at rest is free to rotate about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular…

Three identical spherical shells, each of mass \$m$ and radius \$r$ are placed as shown in the figure. Consider an axis \$XX^{′}$ which is touching the two shells and passing through the diameter of the third shell. The…

An automobile moves on a road with a speed of \$54 km h-1$ . The radius of its wheels is \$0.45\text{m}$ and the moment of inertia of the wheel about its axis of rotation is \$3 kg m2$ . If the vehicle is brought to…