Question

Sol. [Key Concept: Rotational kinematics: revolutions = ω̄·t/2π] $\alpha = \frac{\omega_{2} - \omega_{1}}{\Delta t} = \left( \frac{1200 - 600}{10} \right)\frac{2\pi}{60} = 2\pi rad/s^{2}$

⇒ Use equation of motion, $\omega_{2}^{2} = \omega_{1}^{2} + 2\alpha\theta$

$${\Rightarrow \omega_{2} = 1200 \times \frac{2\pi}{60} = 40\pi }{\omega_{1} = 600 \times \frac{2\pi}{60} = 20\pi }{(40\pi)^{2} = (20\pi)^{2} + 2 \times 2\pi\theta }{\Rightarrow 1200\pi^{2} = 4\pi\theta }$$$\Rightarrow \theta = 300\pi$ radian

⇒ Number of revolution $= \frac{\theta}{2\pi} = 150$