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

In summary, the problem involves finding the angular velocity of gear 5, given the speeds and gear ratios of other gears in the system. The equation used is w5 - wcarrier = (Nring/Nsun)*(wc - wcarrier), where wcarrier is the speed of gear 2 and w5 is the desired angular velocity. However, the incorrect solution indicates that w3, the speed of gear 3, may also be a factor in the calculation. Further examination is needed to correctly solve this problem.
  • #1
Jonski
42
0

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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  • #2
If you're told, "This is a differential," can you re-examine the question productively?
 

1. What is the definition of Angular Velocity?

Angular velocity is the rate of change of angular displacement of an object with respect to time. It is a measure of how fast an object is rotating around a fixed point.

2. How is Angular Velocity measured?

Angular velocity is usually measured in radians per second (rad/s) or degrees per second (deg/s). It can also be measured in revolutions per minute (RPM) or revolutions per second (RPS).

3. What is the formula for calculating Angular Velocity?

The formula for calculating angular velocity is ω = Δθ/Δt, where ω represents angular velocity, Δθ represents change in angular displacement, and Δt represents change in time.

4. How does the size of a gear affect its Angular Velocity?

The size of a gear does not affect its angular velocity. The angular velocity of a gear is determined by its rotational speed and not its size.

5. How does the number of teeth on a gear affect its Angular Velocity?

The number of teeth on a gear does not directly affect its angular velocity. However, the number of teeth can indirectly affect the gear's angular velocity if it is connected to another gear with a different number of teeth, causing a change in rotational speed.

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