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:

Answers (1)

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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