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Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with

angular velocities \omega1 and \omega2. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:

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Law of conservation of angular moment -

vec{	au }= frac{vec{dL}}

- wherein

If net torque is zero

i.e. frac{vec{dL}}= 0

vec{L}= constant

angular momentum is conserved only when external torque is zero .

 

Iw_{1}+Iw_{2} = 2Iw \Rightarrow w=\frac{w_{1}+w_{2}}{2}

\left ( K.E \right )_{i} = \frac{1}{2}Iw_{1}^{2}+\frac{1}{2}w_{2}^{2}

\left (K.E \right )_{f} = \frac{1}{2}\times 2Iw^{2} = I \left ( \frac{w_{1+w_{2}}}{2} \right )^{2}

Loss in K.E = \frac{1}{4}I\left ( w_{1}-w_{2} \right )^{2}

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