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A wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of $15^{0}$ in time t seconds. The angle (in degree) through which it rotates in the next 2t seconds is ______.

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answer is 120.

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Detailed Solution

$\begin{array}{l} θ_{1} = ω_{1} t + \frac{1}{2} α t^{2} \\ 15^{\circ} = 0 + \frac{1}{2} α t^{2} \\ \Rightarrow α t^{2} = 30^{\circ} \end{array}$

$Let angle rotated by wheel in t' seconds be θ_{2}$

$where t^{'} = t + 2 t = 3 t$

$\begin{array}{l} ∴ θ_{2} = ω_{i} t^{'} + \frac{1}{2} α {(t^{'})}^{2} \\ θ_{2} = 0 + \frac{1}{2} α (3 t)^{2} = \frac{9}{2} α t^{2} \\ \Rightarrow θ_{2} = \frac{9}{2} \times 30 = 135^{\circ} \end{array}$

$Increase in angle: Δ θ = θ_{2} - θ_{1} = 135 - 15 = 120^{\circ}$

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