Question

# A particle starts moving in a non-uniform circular motion, has angular acceleration as shown in the figure. The angular velocity at the end of $$4$$ radian is given by $$\omega \ rad/sec$$ then find the value of $$\omega$$.

Solution

## $$\alpha=\dfrac{d\omega}{dt}$$$$\omega=\dfrac{d\theta}{dt}$$$$\implies \omega\dfrac{d\omega}{d\theta}=\alpha$$$$\implies\int \omega d\omega=\int\alpha d\theta=$$area under $$\alpha-\theta$$ graph$$\implies \dfrac{\omega^2}{2}=\dfrac{1}{2}\times 4\times 9$$$$\implies \omega=6rad/s$$Physics

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