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Resultant acceleration Question

  1. Mar 12, 2015 #1
    1. The problem statement, all variables and given/known data
    An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.270rev/s . The magnitude of the angular acceleration is 0.902rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.800m .

    What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t= 0.191s ?

    2. Relevant equations

    (v*v)/r

    Pythagorean theorem


    3. The attempt at a solution

    Tangential acceleration= angular acceleration*radius
    =.902*.400
    =.361

    centripetal acceleration = (v*v)/r
    I calculated v (tangential velocity) to be 1.11 ---which is correct based on answer key
    = (1.11^2)/.400
    =3.08

    sqrt( (3.08^2)+(.361^2) )
    =3.10

    However, this apparently is incorrect. What am I doing wrong?
     
  2. jcsd
  3. Mar 12, 2015 #2

    rude man

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    In calculating tangential velocity and acceleration, are you using correct units for the angular initial speed and acceleration ?
     
  4. Mar 12, 2015 #3
    The method you are followed is correct but not in one point; the question should help:

    What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t= 0.191s ?.

    In an accelerate motion of a point upon a circle its tangential velocity changes continuosly; it is no more the value of the initial istant. So the correct formula to use is (v, v0 and a are tangential):

    v-v0 = at

    t=0.191 s
    a = 0.361 m/s^2
    v0=0.270 x 0.400 = 0.108 m/s
     
  5. Mar 12, 2015 #4

    collinsmark

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    Also, (contrary to the numerical work in Pierce610's post), don't forget to convert revolutions to radians.
     
  6. Mar 12, 2015 #5
    sqrt( (.108^2)+(.361^2) )
    =.38

    Is this the correct set up for the final answer now?
     
  7. Mar 12, 2015 #6

    collinsmark

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    That's not the number I got. Please show your steps, including your units.

    And again, don't forget to convert the revolutions to radians as an early step.
     
  8. Mar 13, 2015 #7
    thanks sincerely to have correct me; I've forgotten to convert them.
     
  9. Mar 14, 2015 #8
    Based on my original post, which step did I mess up

    centripetal acceleration = (v*v)/r
    I calculated v (tangential velocity) to be 1.11 ---which is correct based on answer key
    = (1.11^2)/.400
    =3.08
     
  10. Mar 14, 2015 #9

    ehild

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    Your tangential acceleration is wrong: revolutions have to be converted to radians.
     
  11. Mar 14, 2015 #10

    rude man

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    You had better listen to posts 2, 4 and 9 unless you meant radians instead of revolutions in your original post.
     
  12. Mar 14, 2015 #11
    So I have to convert 1.11 revolutions to radians?
    so would it be 1.11 rev*2piradians/rev ?
     
  13. Mar 14, 2015 #12

    rude man

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    Yes, assuming the 1.11 number was derived correctly (I'm not looking at the problem now).
    In general, take a leaf from this book: all units must be compatible. In most cases for you this means the units of the rationalized mks system, aka SI (Sysème Internationale).
     
  14. Mar 14, 2015 #13

    ehild

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    No.
    The tangential acceleration was wrong. The angular acceleration was given as 0.902 rev/s2. Convert it to radians/s2.
     
  15. Mar 14, 2015 #14
    so .902revs/s^2 *2piradians/rev=1.80pi radians/s^2

    (1.80^2)/.400
    =8.1

    sqrt( (8.1^2)+(.361^2) )
    =8.11

    Is this correct?
     
  16. Mar 14, 2015 #15

    ehild

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    It is wrong. How much is 0.902*2pi?
    How do you get the linear acceleration from the angular acceleration?
     
  17. Mar 14, 2015 #16
    5.67pi ...i dont understand why I keep getting a wrong answer from my calculator. Thanks.


    So 5.67

    (5.67^2)/.400
    =80.37

    sqrt( (80.37^2)+(.361^2) )
    =80.37

    ? this ok now?
     
  18. Mar 14, 2015 #17

    ehild

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    No. Use the units, you will see that it is wrong. What is the unit of the angular acceleration? What is the unit of the linear acceleration?
    What are all those numbers you wrote?
    What do you mean with (5.67^2)/.400? What do you think it is?
     
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