A disc of mass \( M \) and radius \( R \) is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass \( M \) and radius \( \frac{R}{2} \) is fixed to the motor’s thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed \( \omega \). If the angular speed at which the large disc rotates is \( \frac{\omega}{n} \), then the value of \( n \) is __________.
