Question

Consider a Disc of mass 5 kg, radius 2m, rotating with angular velocity of 10 rad/s about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is _____ J.

Answer 1

Correct answer is : 250

\(\vec{L}_i = I \omega _ i = \frac {MR^2}{2}.\omega = 100\,kgm^2/s\)

\(E_i = \frac {1}{2}.\frac {MR^2}{2}.\omega ^2 = 500 J\)

\(\vec{L}_i=\vec {L}_f \Rightarrow 100 = 2I \omega _f\)

\(\omega _f = 5\,rad/sec\)

\(E_f = 2\times \frac {1}{2} . \frac {5 (2)^2}{2}. (5)^2 = 250 J\)

\(\triangle E = 250 J\)