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Force Required by Rockets and Angular Acceleration

  1. Mar 22, 2012 #1
    1. The problem statement, all variables and given/known data
    To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure. (Picture is attached).

    If the satellite has a mass of 4800 kg and a radius of 2.7m , what is the required steady force of each rocket if the satellite is to reach 29 rpm in 6.0 min?

    2. Relevant equations

    F = ma
    ω final - ω initial / t = α
    F/4 = force required by each rocket

    3. The attempt at a solution

    I converted everything to radians, seconds, etc.

    I assumed the initial angular velocity was 0 rad./s.
    3.0368 rad./s / 360 s. = 0.00843 rad./s^2

    The rockets are being fired tangentially so I then found tangential acceleration.
    (2.7 m)(0.00843 rad./s^2) = 0.022761 m/s^2

    Then I used F = ma

    F = (4800 kg)(0.022761 m/s^2)
    F = 109.2528 N

    F/4 = 27 N
     

    Attached Files:

  2. jcsd
  3. Mar 22, 2012 #2

    tms

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    You are mixing translational and rotational equations here. You must stick to rotation. Instead of F = ma, you must use the rotational analog.
     
  4. Mar 22, 2012 #3
    I think I'm a tad bit closer now.

    torque = moment of inertia*angular acceleration

    torque = (4800 kg)*(2.7m)^2*(0.00843 rad./s^2)

    torque = 294.98256 N * m

    Since I want my units to contain only Newtons, shouldn't I divide by the radius?

    294.98256 N * m / 2.7 m = 109.2528 N

    109.2528 N / 4 = 27 N per rocket

    which can't be correct because it's the same as I did before.
     
  5. Mar 22, 2012 #4

    tms

    User Avatar

    You're using the wrong moment of inertia; the spacecraft is a cylinder, not a cylindrical shell.
     
  6. Mar 22, 2012 #5
    tms - Thank you. I obtained the correct answer of about 14 N per rocket.
     
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