How many revolutions does the tub turn while it is in motion?

the tub os a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 8 sec, at which time it is turning at 5 rev/s. at this point, a person opens the lid and the safety turns off the washer. the tub smoothly slows to rest in 12 secs. through how many revolutions does the tub turn while it is in motion?How many revolutions does the tub turn while it is in motion?for spin up cycle, t = 8 , u = 0 , v = 10pi , 胃 = ?

v = u + 伪t

so, 伪 = (v - u)/t = 5pi/4

胃 = 1/2 * 伪t^2 = 1/2 * 5pi/4 * 64 = 40pi = 40pi/2 revs = 20 revs



for spin down cycle, t =12 , u = 10pi , v = 0 , 胃 = ?

v = u + 伪t so, 伪 = - 5pi/6

胃 = 1/2 * 伪t^2 = 1/2 * 5pi/6 * 144 = 60pi = 30 revs



so. total number of revolutions made by the tub is 20 + 30 = 50 revsHow many revolutions does the tub turn while it is in motion?
Total no.of revolutions = Average rev. x time.



For the first 8s, total rev, = 5/2 *8 =20 revolutions.



For the next 12 seconds, total rev. = - [5/2] *12 = - 30.



Total revolutions = 20 - 30 = - 10 revolutions.



It has turned 10 revolutions in the direction opposite ( say anticlockwise) to the direction of rotation while the switch is on( say clockwise)



If we ignore directions then it has moved 20 revolutions in one direction and 30 revolutions in the opposite direction.How many revolutions does the tub turn while it is in motion?Use s = a t^2/2, once for the spin up, again for the spin down, and add.How many revolutions does the tub turn while it is in motion?
this sounds like a hands on experiment to me

hmmmmmmHow many revolutions does the tub turn while it is in motion?The initial angular frequency is w-o = 5*2pi = 10 pi (radians/sec)



The rate of decrease in angular frequency is = -10 pi/12

= -5 pi/6



The angular frequency over time is then:

w(t) = 10pi - 5pi*t/6



The angle covered is the integral:

integral[10pi - 5pi*t/6] {t = 0, 12}

= 10*pi*t - 5*pi*t^2/12 {t = 0, 12}

= 12*10*pi - 5*pi*(12)^2/12

= 120*pi - 60*pi

= 60*pi



Since one revolution = 2*pi

the number of revolutions = 60*pi/(2*pi) = 30.