Hi there!
We can use the angular equivalent of the following kinematic equation:
[tex]\omega_f^2 = \omega_i^2 + 2\alpha \theta[/tex]
ωf = final angular velocity (1.9 rad/s)
ωi = initial angular velocity (11.3 rad/s)
α = angular acceleration (? rad/s²)
θ = angular displacement (17.95 rad)
We can rearrange the equation to solve for angular acceleration.
[tex]\omega_f^2 - \omega_i^2 = 2\alpha \theta\\\\\alpha = \frac{\omega_f^2 - \omega_i^2}{2\theta}[/tex]
Plug in the given values and solve.
[tex]\alpha = \frac{1.9^2 - 11.3^2}{2(17.95)} = \boxed{3.456 \frac{rad}{s}}[/tex]
