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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 $$\omega$$.
1079915_e9641d3d75f74858b666fed76ae60de5.png


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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