A constant torque is applied to a pinion which has a moment of inertia of I_m. The pinion(A) drives two gears, one (B) which is connected to a mass which has a moment of inertia = I_m and the other(C) is connected to a mass which has a moment of inertia = 2I_m. The gear ration R_1=A/B is fixed and is equal to 3. What should the gear ration R_2=A/C be to give the maximum angular acceleration of gear 4? Neglect the mass of the gears.
The Attempt at a Solution
So... Torque out/ Torque in = gear ratio(GR), and I think angular acceleration should be proportional to torque:
So, this would mean that the higher the gear ratio, the higher the torque out, the higher the angular acceleration. Since torque in is fixed and the size of the driver gear A is fixed...
So... the lower the number of teeth on gear C is, the higher the torque and the higher the angular acceleration of gear C. So if there is 0 teeth... should be infinite angular acceleration! So something is obviously wrong...
But the books answer is sqrt(1.8)=1.34.
I have no idea how they got this. Google is not helping. Please help.