Answer:
4.87971 rad/s
Explanation:
[tex]\omega_f[/tex] = Final angular velocity
[tex]\omega_i[/tex] = Initial angular velocity
[tex]\alpha[/tex] = Angular acceleration
[tex]\theta[/tex] = Angle of rotation
Equation of rotational motion
[tex]\omega_f^2-\omega_i^2=2\alpha \theta\\\Rightarrow \alpha=\frac{\omega_f^2-\omega_i^2^2}{2\theta}\\\Rightarrow \alpha=\frac{0^2-3.6^2}{2\times 2\pi \times 1.5}\\\Rightarrow \alpha=-0.68754\ rad/s^2[/tex]
The angular acceleration is -0.68754 rad/s²
[tex]\omega_f^2-\omega_i^2=2\alpha \theta\\\Rightarrow \theta=\frac{\omega_f^2-\omega_i^2^2}{2\alpha}\\\Rightarrow \theta=\frac{2.5^2-3.6^2}{2\times -0.68754}\\\Rightarrow \theta=4.87971\ rad[/tex]
The angle through which the wheel has turned is 4.87971 rad
