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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/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 = 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: Tags 10rev or s, accelerated, rev or s, shaft, uniformly Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post r-soy Physics 1 June 30th, 2012 11:54 AM r-soy Physics 4 June 29th, 2012 09:28 AM summerset353 Real Analysis 1 March 1st, 2010 07:11 PM rose3 Real Analysis 1 December 30th, 2009 04:38 AM floaty Physics 2 February 4th, 2009 07:13 PM

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