Question

question completion status: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 moving to another question will save this response. question 16 of 25 question 16 4 points save answer during the spin - dry cycle of a washing machine, the motor slows from 90 rad/s to 30 rad/s while turning the drum through an angle of 180 radians. what is the magnitude of the angular acceleration of the motor? 32 rad/s² 20 rad/s² 10 rad/s² 64 rad/s²

Explanation:

Step1: Recall angular kinematic formula

Use $\omega_f^2 = \omega_i^2 + 2\alpha\theta$ where $\omega_f=30\,\text{rad/s}$, $\omega_i=90\,\text{rad/s}$, $\theta=180\,\text{rad}$.

Step2: Rearrange for angular acceleration

$\alpha = \frac{\omega_f^2 - \omega_i^2}{2\theta}$

Step3: Substitute values

$\alpha = \frac{30^2 - 90^2}{2\times180} = \frac{900 - 8100}{360} = \frac{-7200}{360} = -20\,\text{rad/s}^2$

Step4: Find magnitude

Magnitude is absolute value of $\alpha$.

Answer:

20 rad/s²