The equation 2(ω1 − ω2) / (ω1 + ω2) represents the _________.

Explanation:

Maximum fluctuation of energy: The difference between the maximum and the minimum energies is known as a maximum fluctuation of energy.

ΔE = Emax - Emin

\( {E_{max}} = {\left( {K.E} \right)_{max}} - {\left( {K.E} \right)_{min}}\)

\(= \frac{1}{2}I\left( {\omega _{max}^2 - \omega _{min}^2} \right)\)

Coefficient of fluctuation of energy:

\({C_E} = \frac{{Maximum\;fluctuation\;of\;energy}}{{Work\;done\;per\;cycle}}\)

Coefficient of fluctuation of speed (CS):

\({C_S} = \frac{{Maximum\;fluctuation\;of\;speed}}{{Mean\;speed}}\)

\({C_S} = \frac{{{\omega _1} - {\omega _2}}}{\omega } = \frac{{2\left( {{\omega _1} - {\omega _2}} \right)}}{{\left( {{\omega _1} + {\omega _2}} \right)}} \)

Mass moment of inertia of the flywheel = I, Mean speed of the rotation = ω, Kinetic energy = E, Coefficient of fluctuation of speed = CS

The maximum fluctuation of energy:

\( {\rm{\Delta }}E = \frac{1}{2}I\omega _1^2 - \frac{1}{2}I\omega _2^2 = \frac{1}{2}I\left( {{\omega _1} + {\omega _2}} \right)\left( {{\omega _1} - {\omega _2}} \right)\)

\({\rm{\Delta }}E = I\omega \left( {{\omega _1} - {\omega _2}} \right) = I{\omega ^2}\frac{{\left( {{\omega _1} - {\omega _2}} \right)}}{\omega } = I{\omega ^2}{C_S}\)

\(E = \frac{1}{2}I{\omega ^2} = \frac{1}{2}\times\frac{{{\rm{\Delta }}E}}{{{C_S}}} = \Delta E\;=2EC_S {{{}}}{{{}}}\)