A wheel is subjected to uniform angular accel | vedclass

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(C) Given that the wheel starts from rest,so initial angular velocity ${\omega _0} = 0$. Let the uniform angular acceleration be $\alpha$.Using the ki

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$3$

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(C) Given that the wheel starts from rest,so initial angular velocity ${\omega _0} = 0$. Let the uniform angular acceleration be $\alpha$.Using the kinematic equation for angular displacement: $	heta = {\omega _0}t + \frac{1}{2}\alpha {t^2}$.For the first $2 \ s$ $(t = 2 \ s)$: ${	heta _1} = 0 + \frac{1}{2}\alpha {(2)^2} = 2\alpha$ ... $(i)$.For the total time of $4 \ s$ $(t = 2 + 2 = 4 \ s)$: ${	heta _1} + {	heta _2} = 0 + \frac{1}{2}\alpha {(4)^2} = 8\alpha$ ... $(ii)$.Subtracting equation $(i)$ from equation $(ii)$: ${	heta _2} = 8\alpha - 2\alpha = 6\alpha$.Now,the ratio is $\frac{{	heta _2}}{{	heta _1}} = \frac{6\alpha}{2\alpha} = 3$.

$A$ wheel is subjected to uniform angular acceleration about its axis. Initially,its angular velocity is zero. In the first $2 \ s$,it rotates through an angle ${\theta _1}$. In the next $2 \ s$,it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}/{\theta _1}$ is:

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