A wheel undergoes a constant angular acceleration from time t = 0 to t = 20 s and thereafter angular acceleration is zero. If angular velocity at t = 2 s is found to be 5 rad / s , then the number of revolutions made by the wheel in time interval t = 0 s to t = 50 s is

Question

A wheel undergoes a constant angular acceleration from time t = 0 to t = 20 s and thereafter angular acceleration is zero. If angular velocity at t = 2 s is found to be 5 rad / s , then the number of revolutions made by the wheel in time interval t = 0 s to t = 50 s is, 1000 / π, 600 π, 1500 / π, 2000 / π

MARKS App · Accepted Answer

From kinematic equations of circular motion, we have ω = ω 0 + α t ⇒ 5 = 0 + α × 2 ⇒ α = 2 . 5 rad s - 2 For total angle rotated, we have θ = θ 1 0 t o 20 s + θ 2 20 t o 50 s ⇒ θ = ω 0 × 20 + 1 2 α × 20 2 + ω × 30 , here ω is angular velocity at t = 20 s ⇒ θ = ω 0 × 20 + 1 2 × α × 20 2 + ω 0 + α × 20 × 30 ⇒ θ = 0 × 20 + 1 2 × 2 . 5 × 20 2 + 0 + 2 . 5 × 20 × 30 ⇒ θ = 500 + 1500 = 2000 ⇒ n × 2 π = 2000 ⇒ n = 1000 π

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