Suppose an external torque T1 is applied to Shaft 1, which has polar area moment of inertia J1. Gear 1 is mounted on Shaft 1 and has a tooth no. N1. Gear 1 drives Gear 2, which has tooth no. N2 and is mounted on Shaft 2, which has a polar moment of inertia J2.
a) Assuming that Shaft 2 carries no torque (it freely spins), and that the inertia of each gear is negligible, determine the angular acceleration of Shaft 2.
b) Find the optimal tooth no. ratio, N2/N1 for maximal angular acceleration of Shaft 2.