Let ω₁, ω₂ and ω₃ be the angular speeds of the second hand, minute hand and hour hand of a smoothly running analog clock. If x₁, x₂ and x₃ are their respective angular distances in 1 minute, which factor remains constant?
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Question

Let ω₁, ω₂ and ω₃ be the angular speeds of the second hand, minute hand and hour hand of a smoothly running analog clock. If x₁, x₂ and x₃ are their respective angular distances in 1 minute, which factor remains constant?

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G1 Physics · Accepted Answer

Step 1: Angular distance in a fixed time interval Δt is x=ωΔt. Step 2: Therefore ω/x = 1/Δt, which is the same for every hand because the interval is the same 1 minute. Step 3: Hence ω₁/x₁ = ω₂/x₂ = ω₃/x₃. Final answer: A. Note: the printed solution on the supplied page lists B, but x=ωΔt gives A.