Question

A certain front-loading washing machine has a drum of diameter 23.3 inches. A small tennis ball placed inside spins in a vertical circle pressed against the inner wall of the drum. How quickly would the drum have to spin (in radians per second) in order to ensure that the tennis ball remained pinned against the wall for the entire cycle without falling off?

Answer 1

33.12 rad/s

Explanation:

We are given that

Diameter=d=23.3 in

Radius,=
`r=(d)/(2)=(23.3)/(2)=11.65 in=11.65* 0.0254= 0.29591 m`

1 in=0.0254 m

We have to find the angular speed of drum would have to spin.

Force=
`mg`

Centripetal force=
`m\omega^2 r`

`mg=m\omega^2 r`

`\omega^2=(g)/(r)`

`\omega=\sqrt{(g)/(r)}`

Where
`g=9.8m/s^2`

`\omega=\sqrt{(9.8)/(0.29591)`

`\omega=33.12 rad/s`