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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