A wheel initially at rest is subjected to a u | vedclass

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(B) The angular displacement is given by the formula $	heta = \frac{1}{2}\alpha t^2$, where $\alpha$ is the uniform angular acceleration and $t$ is t

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$3$

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(B) The angular displacement is given by the formula $	heta = \frac{1}{2}\alpha t^2$, where $\alpha$ is the uniform angular acceleration and $t$ is the time.For the first $2 	ext{ s}$ $(t = 2 	ext{ s})$, the angular displacement is $	heta_1 = \frac{1}{2}\alpha (2)^2 = 2\alpha$.For the total time of $4 	ext{ s}$ $(t = 4 	ext{ s})$, the total angular displacement is $	heta_{	ext{total}} = \frac{1}{2}\alpha (4)^2 = 8\alpha$.The angular displacement in the next $2 	ext{ s}$ is $	heta_2 = 	heta_{	ext{total}} - 	heta_1 = 8\alpha - 2\alpha = 6\alpha$.Therefore, the ratio $\frac{	heta_2}{	heta_1} = \frac{6\alpha}{2\alpha} = 3$.

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

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