A rope is wound round a hollow cylinder of mass $3\;{\rm{ kg }}$ and radius ${\rm{40\;}}\,{\rm{cm}}{\rm{.}}$ What is the angular acceleration of the cylinder if the rope is pulled with a force of ${\rm{30\; N?}}$

Calculate the angular momentum of a body whose rotational energy is 10 Joule. If the angular momentum vector coincides with the axis of rotation and its moment of inertia about this axis is $8 imes {10^{ - 7}}\;kg\;{m^2}$

A solid sphere of mass 2 kg rolls on a smooth horizontal surface at 10 ${\rm{m}}{{\rm{s}}^{ - 1}}$. It then rolls up a smooth inclined plane of inclination ${30^0}$ with the horizontal. The height attained by the sphere before it stops is

A disc rotates with angular velocity $\omega$ and kinetic energy $E$. Then its angular momentum.

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is

A solid sphere of mass 2 kg rolls on a smooth horizontal surface at 10 ${\rm{m}}{{\rm{s}}^{ - 1}}$. It then rolls up a smooth inclined plane of inclination ${30^0}$ with the horizontal. The height attained by the sphere before it stops is

A sphere and a hollow cylinder roll without slipping down two separate inclined planes and travel the same distance in the same time. If the angle of the plane down which the sphere rolls is ${30^0}$. The angle of the other plane is

Two discs of moment of inertia ${I_1}\,and\,{I_2}$ and angular speeds ${\omega _1}\,and\,{\omega _2}$ are rotating along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate combindly along the same axis the rotational KE of system will be

A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?

Given ${\rm{\vec r}} = 4\hat j\,and\,\,{\rm{\vec p}} = 2\hat i + 3\hat j + \hat k$ The angular momentum is

A car travels at $54 \, km/h$. Its wheels have a radius of $0.45 \, m$ and a moment of inertia of $3 \, kg \cdot m^2$. If the car stops in $15 \, s$, what's the average torque applied by the brakes?