A wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of 15 o in time t seconds. The increase in angle through which it rotates in the next 2 t seconds is

Question

A wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of 15 o in time t seconds. The increase in angle through which it rotates in the next 2 t seconds is, 90 o, 120 o, 30 o, 45 o

MARKS App · Accepted Answer

If angular acceleration is constant, we have θ = ω 0 t + 1 2 α t 2 The given θ = 15 o ω 0 = 0 For the first conditions (time = t sec) 15 o = 0 + 1 2 α t 2 ⇒ 15 o = 1 2 α t 2 ......(i) For the second conditions (time = t+2t sec) θ 1 = 1 2 α 3 t 2 = 1 2 α 9 t 2 .......(ii) So for 2t sec, Δ θ = θ 1 - 1 2 α t 2 Δ θ = 9 × 1 2 α t 2 - 1 2 α t 2 = 8 1 2 α t 2 = 8 × 15 o = 120 o (from equation(i))

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