The tub of a washing machine goes into its spin cycle, starting from rest and gaining angular speed steadily for 9.00 s, at which time it is turning at 7.00 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

Explanation:

7 rev /s = 7 x 2π rad /s

angular velocity = 14π rad /s

Angular acceleration α = increase in angular velocity / time

= 14π - 0 / 9

α = 4.8844 rad / s

θ  = 1/2 α x t²   θ is angle of rotation , t is time

= 1/2 x 4.8844  x 9²

= 197.8182 rad

2π n = 197.8182

n = 31.5 rotation

During acceleration , no of rotation made = 31.5

During deceleration :

deceleration =

Angular deceleration α = decrease in angular velocity / time

= 14π - 0 / 13

α = 3.3815  rad / s

θ  = 1/2 α x t²   θ is angle of rotation , t is time

= 1/2 x 3.3815  x 13²

= 285.736 rad

2π n = 285.736

n = 45.5 rotation

total rotation

= 45.5 + 31.5

= 77 .