What is the Angular Velocity of Gear 5 in a Differential Gear System?

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SUMMARY

The angular velocity of gear 5 in a differential gear system is calculated to be 360 rpm, based on the relationship between the gears involved. Gear 2 operates at 80 rpm counterclockwise, while gear 4 is influenced by gear 3, which has an angular velocity of -40 rpm. The calculations utilize the gear tooth ratios, specifically N2=16, N3=32, N4=30, N5=22, and N7=77, to derive the angular velocities. The initial solution was incorrect due to the oversight of gear 3's effect on gear 4, which subsequently impacts gear 5.

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Homework Statement


Gear 2 in the figure below is driven at a speed of 80 rpm in the CCW direction viewed from the right end. Gear 4 meshes with a fixed ring gear (gear 7) and with gear 5. Find the angular velocity of gear 5. N2= 16 T, N3= 32 T, N4= 30 T, N5= 22 T and N7= 77 T.
Question4.png

Homework Equations


w1/w2 = -N2/N1
w = angular velocity
N = number of teeth

(wsun - wcarrier)/(wring - wcarrier) = -Nring/Nsun

The Attempt at a Solution


wcarrier = 80 rpm
wring = 0 as its fixed
wsun = w5

w5 -wc = 77/22 * wc
w5 - 80 = 3.5*80
w5 = 360rpm

This is incorrect however, and I think it is because w3 has an effect on w4 which in turn effects w5.
w3 = -40 = w4;
However I'm not sure how to connect these two values, any help would be much appreciated
 
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