Question

The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 7.00 s, at which time it is turning at 7.00 rev/s. At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub smoothly slows to rest in 12.0 s. Through how many revolutions does the tub turn while it is in motion?

_____________ rev

Answer 1

67 revolutions

Step-by-step explanation:

t = Time taken

`\omega_f` = Final angular velocity

`\omega_i` = Initial angular velocity

`\alpha` = Angular acceleration

`\theta` = Number of rotation

Equation of rotational motion

`\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=(\omega_f-\omega_i)/(t)\\\Rightarrow \alpha=(7-0)/(7)\\\Rightarrow a=1\ rev/s^2`

`\omega_f^2-\omega_i^2=2\alpha \theta\\\Rightarrow \theta=(\omega_f^2-\omega_i^2)/(2\alpha)\\\Rightarrow \theta=(7^2-0^2)/(2* 1)\\\Rightarrow \theta=24.5\ rev`

Number of revolutions in the 7 seconds is 24.5

`\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=(\omega_f-\omega_i)/(t)\\\Rightarrow \alpha=(0-7)/(12)\\\Rightarrow a=-0.583\ rev/s^2`

`\omega_f^2-\omega_i^2=2\alpha \theta\\\Rightarrow \theta=(\omega_f^2-\omega_i^2)/(2\alpha)\\\Rightarrow \theta=(0^2-7^2)/(2* -0.583)\\\Rightarrow \theta=42.02\ rev`

Number of revolutions in the 12 seconds is 42.02

Total total number of revolutions in the 20 second interval is 24.5+42.02 = 66.52 = 67 revolutions