Question

Operating speed of an automatic washing machine is 5.5 rad s-1. After loading
dirty clothes and pressing a start button, the tub of the washer can reach its
operating speed with an average angular acceleration of 4.15 rad s-2. Later at the
spin-dry mode, it is starting from rest and reaching an angular speed of 6.0 revolution per second in 7.0 s.

a) How long does it take for the clothes to come up to the speed during the
washing mode?

b) Now the tub of the washer goes into it spin-dry cycle. At this point, the person
doing the laundry opens the lid and a safety switch turns off the washer. The tub
slows to rest in 13.0 s. How many revolutions does the tub turn during this
20.0 s interval?

Answer 1

(a) The time is

$$t=\frac{\omega_o}{\alpha}=\frac{5.5}{4.15}=1.32\text{ s}.$$

(b) During the 7 s:

$$n_1=\frac{\phi_1}{2\pi}=\frac{\omega_dt_1}{4\pi}=\frac{6·7}{4\pi}=3.$$

During the 13 s:

$$n_2=\frac{\phi_2}{2\pi}=\frac{\omega_dt_2}{4\pi}=\frac{6·13}{4\pi}=6.$$

The total number of revolutions is

$$n=n_1+n_2=9.$$