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May 24th, 2012, 09:58 AM   #1
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A shaft is uniformly accelerated from 10rev/s to 18 rev/s in

A shaft is uniformly accelerated from 10rev/s to 18 rev/s in 4 sec .
The shaft continues to accelerate at this rate for the next 8 sec . Thereafter the shaft rotates with a uniform angular speed . Find the total time to complete 400 rev .

[color=#FF40BF]my answer is ...[/color]

10 rev/s----------------18rev/s-------------------
4s
W0 = 62.83 rad/s
Wf = 113.0
total time at 400 rev ========400/2Pi
so Q = 2513 rad
w = w0 + at
133.0 = 62.83 + at
a = 12.4 so this is niforml accelerated
now I will take the velocity at 12 sec (4+8 = 12 )
so
w = w0 + w
w = 113.0 + 12.4 X (12)
=261.8

------------ now I will take time after 12 s which the a = 0 because of angular speed ----

Q = w0 +1/2 at^2
2513=261.8t+1/2(0)^2 t
t= 9.5 s

so Total time = 12 + 9.5 = 21.5 s



t = 2513/261.8 =
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May 24th, 2012, 10:45 AM   #2
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Re: A shaft is uniformly accelerated from 10rev/s to 18 rev/

We are given:

where

for

Hence:



Thus, the number of revolutions in the first 12 second is:



The angular velocity at is:

hence:



Now, for we have:

where

Hence:



Setting we find:







Thus, the total time in seconds is:

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May 24th, 2012, 02:38 PM   #3
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Re: A shaft is uniformly accelerated from 10rev/s to 18 rev/

Markfl sorry ..I have confusing ,, why solve the Q in this way

why you don't use this formula

for rotating motion

w = w0 + at
w^2 = wo^2 + 2 a Q
Q = ut + 1/2Q t^2

which I did ?
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May 25th, 2012, 09:29 AM   #4
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Re: A shaft is uniformly accelerated from 10rev/s to 18 rev/

If you'll notice, I used/derived the same formulas, I just used the variables I was taught to use:

? for the angle

? for the angular velocity

So, just substitute for these the variables you like.
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May 26th, 2012, 01:14 PM   #5
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Re: A shaft is uniformly accelerated from 10rev/s to 18 rev/

Hi the teacher said here t = 16 s
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May 26th, 2012, 03:32 PM   #6
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Re: A shaft is uniformly accelerated from 10rev/s to 18 rev/

What is your teacher's reasoning?

edit: I found my error and corrected my post above.
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May 26th, 2012, 06:02 PM   #7
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Re: A shaft is uniformly accelerated from 10rev/s to 18 rev/

We need not convert from revolutions to radians.

We are given:

where

for

Hence:



Thus, the number of revolutions in the first 12 seconds is:



The angular velocity at is:

hence:



Now, for we have:

where

Hence:



Setting we find:





Thus, the total time in seconds is:

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