in the above question I have doubt regarding validity of angular momentum conservation. The question is solved by conserving angular momentum about axis of larger disc as follows; 0=−12M(R2)2w+M(Rw′)R+12M(R2)w′w′=w120 = -\frac{1}{2} M(\frac{R}{2})^2 w + M(Rw')R + \frac{1}{2} M(R^2)w' w'=\frac{w}{12} but as the smaller disc is operated by motor, is angular momentum conserved when motor is turned on For example: if two similar discs are put one on one, and one of them is operated by motor giving a constant angular velocity ww , both will move in same direction with ww . and angular momentum is not conserved please clear doubt.