A rigid body is rotating with variable angula | vedclass

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(B) The angular velocity is given by $\omega = a - bt$.To find the time $t$ when the body comes to rest,we set $\omega = 0$:$a - bt = 0 \implies t = \

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$\frac{a^2}{2b}$

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(B) The angular velocity is given by $\omega = a - bt$.To find the time $t$ when the body comes to rest,we set $\omega = 0$:$a - bt = 0 \implies t = \frac{a}{b}$.The total angle $	heta$ subtended is the integral of angular velocity with respect to time from $t = 0$ to $t = \frac{a}{b}$:$	heta = \int_{0}^{a/b} (a - bt) dt$.Integrating the expression:$	heta = \left[ at - \frac{bt^2}{2} ight]_{0}^{a/b}$.Substituting the limits:$	heta = a\left(\frac{a}{b}ight) - \frac{b}{2}\left(\frac{a}{b}ight)^2$.$	heta = \frac{a^2}{b} - \frac{b}{2} \cdot \frac{a^2}{b^2} = \frac{a^2}{b} - \frac{a^2}{2b}$.$	heta = \frac{2a^2 - a^2}{2b} = \frac{a^2}{2b}$.

$A$ rigid body is rotating with variable angular velocity $\omega = (a - bt)$ at any instant of time $t$. The total angle subtended by it before coming to rest will be ($a$ and $b$ are constants).

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