The sum of two numbers is 17, and their difference is 29. What are the two numbers?
2 answers:
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The two gears are shown n the diagram below.
ω₁ and ω₂ are the angular velocities of the larger and smaller gears respectively.
Part 1.
When the smaller gear makes one revolution, it turns through an angle of 2π radians or 360°.
Because the gears do not slip, the larger gear turns through an angle of θ, so that
(θ radians)*(8 in) = (2π radians)*(2 in)
or
8θ = 4π
θ = π/2 radians = 90°
Answer: 90.0°
Part 2.
When the larger gear makes one revolution, it turns through an angle of 2π radians.
Because the gears do not slip, the smaller gear turns through an angle φ, such that
(2 in)*(φ radians) = (8 in)*(2π radians)
or
2φ = 16π
φ = 8π radians
= (8π radians)*(1/2π rotations/radian)
= 4 rotations
Answer: 4 rotations
ω₁ and ω₂ are the angular velocities of the larger and smaller gears respectively.
Part 1.
When the smaller gear makes one revolution, it turns through an angle of 2π radians or 360°.
Because the gears do not slip, the larger gear turns through an angle of θ, so that
(θ radians)*(8 in) = (2π radians)*(2 in)
or
8θ = 4π
θ = π/2 radians = 90°
Answer: 90.0°
Part 2.
When the larger gear makes one revolution, it turns through an angle of 2π radians.
Because the gears do not slip, the smaller gear turns through an angle φ, such that
(2 in)*(φ radians) = (8 in)*(2π radians)
or
2φ = 16π
φ = 8π radians
= (8π radians)*(1/2π rotations/radian)
= 4 rotations
Answer: 4 rotations