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Question

${E_i} = \frac{1}{2}{I_1} 	imes \omega _1^2 + \frac{1}{2}\frac{I}{2} 	imes \frac{{\omega _1^2}}{4}$

$ = \frac{{{I_1}\omega _1^2}}{2}\left( {\frac

Vedclass · Accepted Answer

$ - \frac{{{I_1}\omega _1^2}}{{24}}$

Vedclass · Answer

${E_i} = \frac{1}{2}{I_1} 	imes \omega _1^2 + \frac{1}{2}\frac{I}{2} 	imes \frac{{\omega _1^2}}{4}$

$ = \frac{{{I_1}\omega _1^2}}{2}\left( {\frac{9}{8}} ight) = \frac{9}{{16}}{I_1}\omega _1^2$

${I_1}{\omega _1} + \frac{{{I_1}\omega { _1}}}{4} = \frac{{3{I_1}}}{2}\omega \,\,\,;\,\,\,\frac{5}{4}{I_1}{\omega _1} = \frac{{3{I_1}}}{2}\omega $

$\omega  = \frac{5}{6}{\omega _1}\,\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,{E_f} = \frac{1}{2} 	imes \frac{{3{I_1}}}{2} 	imes \frac{{25}}{{36}}\omega _1^2$

$ = \frac{{25}}{{48}}{I_1}\omega _1^2$

$ \Rightarrow {E_f} - {E_i} = {I_1}\omega _1^2\frac{{25}}{{49}} - \frac{{ - 2}}{{48}}{I_2}\omega _1^2$

$ = \frac{{25}}{{48}}{I_1}\omega _1^2$

$ \Rightarrow {E_f} - {E_i} = {I_1}\omega _1^2\left( {\frac{{25}}{{48}} - \frac{9}{{16}}} ight) = \frac{{ - 2}}{{48}}{I_1}\omega _1^2$

$ = \frac{{ - {I_1}\omega _1^2}}{{24}}$

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