Question

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In this first 2 sec, it rotates through an angle θ₁; in the next 2 sec, it rotates through an additional angle θ₂. The ratio of θ₂/θ₁ is

Moderate

Solution

$\begin{array}{l} θ = ω_{0} t + \frac{1}{2} {αt}^{2} . Here ω_{0} = 0 \\ θ_{1} = \frac{1}{2} α (2)^{2} = 2 α \\ θ_{2} = \frac{1}{2} α (4)^{2} - θ_{1} = 8 α - 2 α = 6 α \\ ∴ \frac{θ_{2}}{θ_{1}} = \frac{6 α}{2 α} = 3 \end{array}$

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