Question

inside a washing machine, the radius of the cylinder where the clothes sit is 0.50 m. in one of its settings the machine spins the cylinder at 2.0 revolutions per second. what is the acceleration of an item of clothing?

Answer 1

Approximately
`79\; {\rm m\cdot s^(-2)}`.

Step-by-step explanation:

Apply unit conversion and ensure that angular velocity
`\omega` is in radians per second. The angular displacement of each revolution is
`2\, \pi` radians. Therefore:

`\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}`.

The clothes in this laundry machine are in a centripetal motion. The radius of the motion is
`r = 0.50\; {\rm m}`, and the angular velocity of the clothes is
`\omega \approx 12.566\; {\rm s^(-1)}`. The acceleration of the clothes will be:

`\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}`.