Question

1. determine the angular acceleration of a propeller that accelerates from 800 rpm to 200 rpm in 4 seconds.

\\( 15.71 \frac{\text{rad}}{\text{s}^2} \\)
\\( -15.71 \frac{\text{rad}}{\text{s}^2} \\)
\\( -7.86 \frac{\text{rad}}{\text{s}^2} \\)
\\( 7.86 \frac{\text{rad}}{\text{s}^2} \\)

Explanation:

Step1: Convert initial RPM to rad/s

$\omega_0 = 800 \times \frac{2\pi}{60} = \frac{80\pi}{3} \approx 83.78 \frac{\text{rad}}{\text{s}}$

Step2: Convert final RPM to rad/s

$\omega_f = 200 \times \frac{2\pi}{60} = \frac{20\pi}{3} \approx 20.94 \frac{\text{rad}}{\text{s}}$

Step3: Apply angular acceleration formula

$\alpha = \frac{\omega_f - \omega_0}{t} = \frac{\frac{20\pi}{3} - \frac{80\pi}{3}}{4} = \frac{-\frac{60\pi}{3}}{4} = \frac{-20\pi}{4} = -5\pi \approx -15.71 \frac{\text{rad}}{\text{s}^2}$

Answer:

$-15.71 \frac{\text{rad}}{\text{s}^2}$