Systems of Particles and Rotational Motion — Physics STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSystems of Particles and Rotational Motion2 Marks
Question
Obtain $\omega=\omega_0+\alpha t$ from first principles.
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Answer
The angular acceleration is uniform, hence $ \frac{ d \omega}{ d t}=\alpha=\text { constant } \quad\quad\text{(i)} $
Integrating this equation, $ \begin{aligned} \omega & =\int \alpha d t+c \\ & =\alpha t+c \quad \text { (as } \alpha \text { is constant) } \end{aligned} $
At $t=O, \omega=\omega_0$ (given) From (i) we get at $t=O, \omega=c=\omega_0$ Thus, $\omega=\alpha t+\omega_0$ as required. With the definition of $\omega= d \theta / d t$ we may integrate Eq. (6.36) to get Eq. (6.37). This derivation and the derivation of Eq. (6.38) is left as an exercise.
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