Question

1. a washing machine drum during a spin cycle can spin up to 800 rpm. if it takes the drum 5 seconds to reach the top speed from rest, what is the acceleration of the washing machine drum?\\(\bigcirc\\) \\(\frac{83.78\\ \text{rad}}{s^2}\\)\\(\bigcirc\\) \\(\frac{16.76\\ \text{rad}}{s^2}\\)\\(\bigcirc\\) \\(\frac{41.89\\ \text{rad}}{s^2}\\)\\(\bigcirc\\) \\(\frac{8.38\\ \text{rad}}{s^2}\\)

Explanation:

Step1: Convert rpm to rad/s

First, convert 800 rpm to radians per second.
1 revolution = $2\pi$ radians, 1 minute = 60 seconds.
$\omega = 800 \times \frac{2\pi}{60} = \frac{80\pi}{3} \approx 83.78$ rad/s

Step2: Calculate angular acceleration

Use $\alpha = \frac{\omega - \omega_0}{t}$, where $\omega_0=0$ (starts from rest), $t=5$ s.
$\alpha = \frac{83.78 - 0}{5} = 16.76$ $\frac{\text{rad}}{s^2}$

Correction Note: The correct calculation for $\omega$ is $800 \times \frac{2\pi}{60} \approx 83.78$ rad/s, then acceleration $\alpha = \frac{83.78}{5} = 16.76$ $\frac{\text{rad}}{s^2}$

Corrected Final Answer:

16.76 $\frac{\text{rad}}{s^2}$

Answer:

83.78 $\frac{\text{rad}}{s^2}$