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May 24th, 2012, 09:58 AM  #1 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  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/s18rev/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 = 
May 24th, 2012, 10:45 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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: 
May 24th, 2012, 02:38 PM  #3 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  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 ? 
May 25th, 2012, 09:29 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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. 
May 26th, 2012, 01:14 PM  #5 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  Re: A shaft is uniformly accelerated from 10rev/s to 18 rev/
Hi the teacher said here t = 16 s

May 26th, 2012, 03:32 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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. 
May 26th, 2012, 06:02 PM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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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10rev or s, accelerated, rev or s, shaft, uniformly 
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