An air compressor is powered by a $200\,rad\,s^{-1}$ electric motor using a $V-$ belt drive. The motor pulley is $8\,cm$ in radius, and the tension in the $V-$ belt is $135\,N$ on one side and $45\,N$ on the other. The power of the motor will be ...... $kW$.

A flywheel has moment of inertia $4\ kg - {m^2}$ and has kinetic energy of $200\ J$. Calculate the number of revolutions it makes before coming to rest if a constant opposing couple of $5\ N - m$ is applied to the flywheel .......... $rev$

A uniform cylinder of radius $R$ is spinned with angular velocity  $\omega$ about its axis and then placed into a corner. The coefficient of friction between the cylinder and planes is $μ$. The number of turns taken by the cylinder before stopping is given by

$A$ rod hinged at one end is released from the horizontal position as shown in the figure. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then the maximum angle $‘\theta ’$ made by the hinged upper half with the vertical is ......... $^o$.

A rod of length $1\,meter$ is standing vertically, when its other end touches the ground without slipping then the speed of other end will be

A particle performs uniform circular motion with an angular momentum $L.$  If the angular frequency of the particle is doubled and kinetic energy is halved, its angular momentum becomes