Question 30

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s, it rotates through an angle $$\theta_1$$. In the next 2 s, it rotates through an angle $$\theta_2$$. Then the ratio $$\frac{\theta_2}{\theta_1}$$ is :

$$\theta = \omega_0 t + \frac{1}{2}\alpha t^2$$

$$\theta = \frac{1}{2}\alpha t^2$$

$$\theta_1 = \frac{1}{2}\alpha (2)^2 = \frac{1}{2}\alpha (4) = 2\alpha$$

$$\theta_{\text{total}} = \frac{1}{2}\alpha (4)^2 = \frac{1}{2}\alpha (16) = 8\alpha$$

$$\theta_2 = \theta_{\text{total}} - \theta_1$$

$$\theta_2 = 8\alpha - 2\alpha = 6\alpha$$

$$\frac{\theta_2}{\theta_1} = \frac{6\alpha}{2\alpha} = 3$$

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