A particle starts from rest with constant angular acceleration. It completes N₁ revolutions during the first t seconds and N₂ revolutions during the next t seconds. Then N₁: N₂ is:
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A particle starts from rest with constant angular acceleration. It completes N₁ revolutions during the first t seconds and N₂ revolutions during the next t seconds. Then N₁:N₂ is:

G1 Physics · Accepted Answer

With constant angular acceleration and zero initial angular speed, angular displacement θ=½αt². In the first interval, θ₁=½αt². Total displacement in 2t is ½α(2t)²=2αt². Hence displacement in the second interval is θ₂=2αt²−½αt²=3/2 αt². Therefore θ₁:θ₂=1:3, and the same ratio holds for revolutions.