What is the relation between the angular velocities of Gear

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Direction: A planetary gear train has four gears and one carrier. Angular velocities of the gears are ω₁, ω₂, ω₃, and ω₄, respectively. The carrier rotates with angular velocity ω₅

What is the relation between the angular velocities of Gear 1 and Gear 4?

1. ω₁ - ω₅ = 6
  ω₄ - ω₅
2. ω₄ - ω₅ = 6
  ω₁ - ω₅
3. ω₁ - ω₂ = - 3/3
  ω₄ - ω₅
4. ω₂ - ω₅ = 8/9
  ω₄ - ω₅

Correct Option: A

	ω₁ - ω₅	= 3
	ω₂ - ω₅

(with respect to arm 5 or carrier 5)

	ω₃ - ω₅	= 2
	ω₄ - ω₅

(with respect to carrier 5)
As ω₃ = ω₂

∴	ω₁ - ω₅	= 6
	ω₄ - ω₅