The Tub of a washer goes into a spin cycle, starting from rest and gaining angular speed steadily for 8 s, when it is turning at 5 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 12s. Through how many revolutions does the Tub turn while it is in motion?(adsbygoogle = window.adsbygoogle || []).push({});

Ok, I am going to do this problem in 2 stages: One for Wi =0 and Wf=5 rev/s and the second for Wi=5rev/s and W[size=.5]f[/size]=0

First stage:

Known

Wi=0

Wf=5 rev/s

T=0

T=8s

Oi=0

Unknown

A=?

Of=?

Wf= (5 rev/s)(2(pi)rad/rev)

Wf= 10(pi) rad or 31.4 rad

A = (Wf-Wi)/T

A = 31.4/8

A = 3.9 rad/(s^2)

Of=Oi+(Wi(T)+.5(A)(T)^2

Of= 0 + (10)(pi)(8) + .5(3.9)(8)^2

Of= 80(pi) + 40(pi)

Of= 377 rad (I am going to leave it in this form because I am going to have to plug it into stage two.

Stage two:

Known

Wf= 0

Wi= 5 rev/s or 10(pi) rad/s

Oi= 377 rad (found in stage one)

T=12 s

Unkown

A=?

Of=?

A = (Wf-Wi)/T

A = (0-31.4)/12

A = -2.6 rad/s^2

Of=Oi+(Wi)(T)+.5(A)(T)^2

Of= 377 + 31.4(12) + .5(-2.6)(12)^2

Of= 377 + 376.8 - 187.2

Of=566.8 rad

Now we need to convert to revolutions:

566.8 rad(57.3/rad)= 32477.64 degrees

32477.64/(360/rev) = 90. 2 rev

Ok here is what I do not get.

My revolutions for the washer when its acceleration is increasing in stage one is slower than the revolutions when the acceleration is decreasing in stage two. I think I am correct but it doesn't make sense.

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# Rotational Kinematics Help (constant angular acceleration)

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