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(C) Given the angular velocity $\omega(t) = \alpha - \beta t$.At time $t = 0$,$\omega = \alpha$.The body comes to rest when $\omega(t) = 0$.$\alpha -

Vedclass · Accepted Answer

$\frac{\alpha^2}{2 \beta}$

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(C) Given the angular velocity $\omega(t) = \alpha - \beta t$.At time $t = 0$,$\omega = \alpha$.The body comes to rest when $\omega(t) = 0$.$\alpha - \beta t = 0 \implies t = \frac{\alpha}{\beta}$.The angular displacement $	heta$ is given by the integral of angular velocity with respect to time:$	heta = \int_{0}^{t} \omega(t) dt = \int_{0}^{\alpha/\beta} (\alpha - \beta t) dt$.$	heta = [\alpha t - \frac{1}{2} \beta t^2]_{0}^{\alpha/\beta}$.Substituting the limits:$	heta = \alpha(\frac{\alpha}{\beta}) - \frac{1}{2} \beta (\frac{\alpha}{\beta})^2$.$	heta = \frac{\alpha^2}{\beta} - \frac{1}{2} \frac{\alpha^2}{\beta} = \frac{\alpha^2}{2 \beta}$.

$A$ rigid body rotates about a fixed axis with variable angular velocity $\omega(t) = \alpha - \beta t$ at time $t$,where $\alpha$ and $\beta$ are constants. The angle through which it rotates before it comes to rest is

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