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 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 . If the angular speed at which the large disc rotates is /n, then the value of n is . [figure]
Answer
12
Solution
Key idea: motor torques are internal; no external torque about the fixed vertical axis of the large disc ⇒ angular momentum about it stays zero.
Let the large disc turn with (one sense) and the small disc spin with (ground frame, opposite sense).
Large disc: L1= MR22 . Small disc's centre moves on a circle of radius R: orbital part MR2 .
Spin of small disc: M(R/2)22 = MR28 .
MR22 +MR2 = MR28 ⇒ = 12.
Answer: 12