two situations are illistrated: a moment Mk that\'s being directly applied to ge
ID: 1819019 • Letter: T
Question
two situations are illistrated: a moment Mk that's being directly applied to gear 2 (case 1) and a simple transmission (case 2) in which the moment M is applied to a small gear (gear 1), which then acts on gear 2. I1=0. Gear 2 has mass m and mass moment of inertia I2
a. calculate the acceletration of gear 2 for case 1
b. calculate the acceleration of the gear 2 for case 2
Explanation / Answer
(a) The angular acceleration of the gear 2 in case 1 = M/ I2 (b) For the case 2, considering torque balancing, we have M1 + M2 = 0 M1 = M => M2 = -M When a Moment M is applied on a rotating body, the angular acceleration is given by M/I In case 2, the moment is applied to gear 1 which has I1 = 0 (as specified in the problem). This makes the angular acceleration of gear 1 to be infinite. Inotherwords, the angular acceleration of gear 2 must also be infinite which is an impossible case as based on the inputs given, angular acceleration of gear 2 must be M/I2 (C) Based on the above results, case 2 is impossible for the angular acceleration is infinite while that for case 1, the angular acceleration is clockwise.
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