Answer:
Approximately [tex]79\; {\rm m\cdot s^{-2}}[/tex].
Explanation:
Apply unit conversion and ensure that angular velocity [tex]\omega[/tex] is in radians per second. The angular displacement of each revolution is [tex]2\, \pi[/tex] radians. Therefore:
[tex]\begin{aligned} \omega &= \frac{2.0\; \text{revolution}}{1\; {\rm s}} \\ &= \frac{2.0\; \text{revolution}}{1\; {\rm s}} \, \frac{2\, \pi}{1\; \text{revolution}} \\ &= (4.0\, \pi)\; {\rm s^{-1}} \\ &\approx 12.566\; {\rm s^{-1}}\end{aligned}[/tex].
The clothes in this laundry machine are in a centripetal motion. The radius of the motion is [tex]r = 0.50\; {\rm m}[/tex], and the angular velocity of the clothes is [tex]\omega \approx 12.566\; {\rm s^{-1}}[/tex]. The acceleration of the clothes will be:
[tex]\begin{aligned}a &= \omega^{2} \, r \\ &\approx (12.566\; {\rm s^{-1}})^{2} \, (0.50\; {\rm m}) \\ &\approx 79\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].
