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Question

(C) The angular displacement formula is given by $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$. Given that the initial angular velocity $\omega_0 = 0

Vedclass · Accepted Answer

$1/3$

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(C) The angular displacement formula is given by $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$. Given that the initial angular velocity $\omega_0 = 0$,the formula simplifies to $	heta = \frac{1}{2} \alpha t^2$. For the first $2 \, s$ $(t = 2 \, s)$: ${	heta _1} = \frac{1}{2} \alpha (2)^2 = 2 \alpha$. For the total time of $4 \, s$ $(t = 2 + 2 = 4 \, s)$: ${	heta _1} + {	heta _2} = \frac{1}{2} \alpha (4)^2 = 8 \alpha$. Subtracting the first equation from the second: ${	heta _2} = 8 \alpha - 2 \alpha = 6 \alpha$. Therefore,the ratio $\frac{{	heta _1}}{{	heta _2}} = \frac{2 \alpha}{6 \alpha} = \frac{1}{3}$.

$A$ wheel rotates with a constant angular acceleration. The initial angular velocity is zero. It covers an angular displacement of ${\theta _1}$ in the first $2 \, s$ and ${\theta _2}$ in the next $2 \, s$. Then,the ratio $\frac{{\theta _1}}{{\theta _2}}$ is equal to:

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