Two coaxial discs, having moments of inertia I 1 and I 1 2 , are rotating with respective angular velocities ω 1 and   ω 1 2 , about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If E f and E i are the final…

Question

Two coaxial discs, having moments of inertia I 1 and I 1 2 , are rotating with respective angular velocities &#969; 1 and &#160; &#969; 1 2 , about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If E f and E i are the final and initial total energies, then E f - E i is:

Aicharya · Accepted Answer

As external torque is zero, angular momentum remains conserved.

I_{1} ω_{1} + \frac{I_{1}}{2} \frac{ω_{1}}{2} = (I_{1} + \frac{I_{1}}{2}) ω

∴

Common angular velocity

ω = \frac{5 ω_{1}}{6}

∴

E_{f} - E_{i} = \frac{1}{2} \times (I_{1} + \frac{I_{1}}{2}) ω^{2} - \frac{1}{2} \times I_{1} ω_{1}^{2} - \frac{1}{2} \times \frac{I_{l}}{2} {(\frac{ω_{1}}{2})}^{2}

= \frac{1}{2} \times \frac{3 I_{1}}{2} {(\frac{5}{6} ω_{1})}^{2} - \frac{9}{16} I_{1} ω_{1}^{2}

= \frac{75 I_{1} ω_{1}^{2} - 81 I_{1} ω_{1}^{2}}{144}

= - \frac{6 I_{1} ω_{1}^{2}}{144}

= - \frac{I_{1} ω_{1}^{2}}{24}

Two coaxial discs, having moments of inertia I 1 and I 1 2 , are rotating with respective angular velocities…

Solution