# A Rigid Body Rotates About A Fixed Axis With Variable Angular Velocity Equal To (A Bt) At T Where A And B Are Constants. The Angle Through Which It Rotates Before It Comes To Rest Is

$$\omega = a – bt = 0$$ $$t = \frac{a}{b}$$ $$\Theta = \int \omega dt = \int_{0}^{ab} (a – bt)dt$$ $$\Rightarrow [at – \frac{bt^{2}}{2}]^{\frac{a}{b}}$$ $$\Rightarrow a * \frac{a}{b} – \frac{b}{2} [\frac{a^{2}}{b^{2}}]$$ $$\Rightarrow \frac{a^{2}}{2b}$$

Therefore, angle through which it rotates before it comes to rest is$$\frac{a^{2}}{2b}$$

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