Maximum fluctuation of kinetic energy in an engine has been calculated to be $$2600$$ J. Assuming that the engine runs at an average speed of $$200$$ rpm, the polar mass moment of inertia ( in kg.m² ) of a flywheel to keep the speed fluctuation within $$\, \pm 0.5\% $$ of the average speed is _______ .

Consider a flywheel whose mass $$M$$ is distributed almost equally between a heavy, ring-like rim of radius $$R$$ and a concentric disk-like feature of radius $$R/2$$. Other parts of the flywheel, such as spokes, etc, have negligible mass. The best approximation for $$\alpha ,$$ if the moment of inertia of the flywheel about its axis of rotation is expressed as $$\,\alpha M{R^2},\,\,$$ is ________.

A flywheel connected to a punching machine has to supply energy of $$400$$ Nm while running at a mean angular speed of $$20$$ rad/s. If the total fluctuation of speed is not to exceed $$ \pm 20\% $$, the mass moment of inertia of the flywheel in kg-m² is

The speed of an engine varies from $$210$$ rad/s to $$190$$ rad/s. During cycle the change in kinetic energy is found to be $$400$$ Nm. The inertia of the flywheel in kgm² is