Question

1. given: change in angle (δθ): 900 rad change in time (δt): 3.00 s wanted: angular acceleration (α) in rad/s²? 200 rad/s² 214 rad/s² 240 rad/s² 258 rad/s²

Explanation:

Step1: Recall the formula for angular acceleration

The formula for angular acceleration \(\alpha=\frac{\Delta\theta}{\Delta t^{2}}\) (assuming the object starts from rest, so the initial angular velocity \(\omega_{0} = 0\) and using the kinematic equation \(\Delta\theta=\omega_{0}t+\frac{1}{2}\alpha t^{2}\)).

Step2: Substitute the given values

We are given \(\Delta\theta = 900\) rad and \(\Delta t=3.00\) s. Substituting into the formula \(\alpha=\frac{2\Delta\theta}{\Delta t^{2}}\) (derived from \(\Delta\theta=\frac{1}{2}\alpha t^{2}\) when \(\omega_{0} = 0\)), we get \(\alpha=\frac{2\times900}{3^{2}}\).
First, calculate \(3^{2}=9\), then \(2\times900 = 1800\).
Now, \(\alpha=\frac{1800}{9}=200\) rad/s².

Answer:

200 rad/s²