Question

1. given: final angular velocity (ω₁): 30.0 rad/s change in angle (δθ): 90.0 rad wanted: angular acceleration (α) in rad/s²? 4.10 rad/s² 4.60 rad/s² 5.00 rad/s² 5.35 rad/s²

Explanation:

Step1: Recall the angular kinematic equation

$$\omega_{f}^{2}=\omega_{i}^{2}+2\alpha\Delta\theta$$
Assume the initial angular velocity \(\omega_{i} = 0\) (not given otherwise, so a common assumption for problems where only final velocity, displacement and acceleration are involved). Then the equation simplifies to \(\omega_{f}^{2}=2\alpha\Delta\theta\).

Step2: Solve for \(\alpha\)

Rearrange the equation \(\alpha=\frac{\omega_{f}^{2}}{2\Delta\theta}\).
Substitute \(\omega_{f} = 30.0\space rad/s\) and \(\Delta\theta=90.0\space rad\) into the formula:
$$\alpha=\frac{(30.0)^{2}}{2\times90.0}$$
$$\alpha=\frac{900}{180}$$
$$\alpha = 5.00\space rad/s^{2}$$

Answer:

\(5.00\space rad/s^{2}\)