Suppose an external torque T1 is applied to Shaft 1, which has polar area moment

Question

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.

Explanation / Answer

a>. we have angular acceleration of shaft 2=T1N2/J1N1.........................B>. N2/N2=J2/J1

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