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Centripetal acceleration changing radians/s into rpm's

  1. Apr 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Centrifugal castings- a copper sleeve of inner radius 2.10 cm and outer radius 2.20 cm is to be cast. To eliminate bubbles and give high structural integrity, the centripetal acceleration of each bit of metal should be 100g. What rate of rotation is required? State answer in revolutions per minute.


    2. Relevant equations r=radius, ac=centripetal acceleration, ω=angular speed, g=gravity.
    What I have right now is: ac=rω2, so every particle must undergo 100g of acceleration giving ac=100g or rω2=100g reduced to;
    ω=√100(9.8m/s)/2.10 x 10-2m
    the conversion factor will be the answer in rads/s (1rev/2π)(60s/1min)


    3. The attempt at a solution
    My problem is converting this into radians per second then into rpm's. I am not looking for the answwer per say, but how to put this into my Ti-83 plus and doing the math. I also need to be able to show my work in long hand and just throwing out an answer will not work. I tried using the r from the angle setting and using both radians and degree mode, I looked in the manual but it use of no use. I am sure I am just overlooking something simple, any help would be great.

    Thanks and have a great day.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 15, 2012 #2
    Oops, I obviously made a mental/keystroke error. I believe I got it right, I have:
    ω=√100g/2.10 x 10-2m
    ω=216 rads/s=rpm=216rads/s(1rev/2∏rad)(60.0s/1min)=216(30/∏) leaving rpm's
    216rads/s=2.06 x 103 rev/min
    If you happen to see any mistakes, feel free to comment,

    Thanks and have a great day,
    m
     
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