Question

The tub of a washing machine goes into its spin cycle, starting from rest and gaining angular speed steadily for 10.0 s, at which time it is turning at 6.00 rev/s. At this point, the lid of the washing machine is opened, and a safety switch turns it off. The tub then smoothly slows to rest in 13.0 s. Through how many revolutions does the tub rotate while it is in motion?

Answer 1

69 revolutions

Step-by-step explanation:

given,

initial angular velocity = 0

final angular velocity = 6 rev/s

when safety switch turned off

tub smoothly slows to rest in (t)= 13 s

total revolution of tub = ?

angular acceleration =
`(\omega_f-\omega_0)/(t)`

angular acceleration =
`(6-0)/(10)`

= 0.6 rev/s²

now,

`\theta = \omega_i t +(1)/(2)\alpha t^2`

`\theta = 0+(1)/(2)* 0.6 * 10^2`

= 30 revolution

now,

when safety switch turn off

angular acceleration =
`(\omega_f-\omega_0)/(t)`

angular acceleration =
`(0-6)/(13)`

= -0.462 rev/s²

now,

`\theta = \omega_i t +(1)/(2)\alpha t^2`

`\theta = 6 * 13 -(1)/(2)* 0.462 * 13^2`

= 39 revolution

total revolution = 30 + 39 = 69 revolutions.

tub will rotate 69 revolutions