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Angular velocity and acceleration

  1. Jun 19, 2004 #1
    Hey i have this problem and would like to know if what i got is somewhere in the right direction. Any help would be GREATLY appreciated

    A gymnast is performing a forward double somersault.

    The gymnast’s initial angular velocity is 0 rad/s.
    The gymnast generates a 115 N-m torque.
    The torque is applied to the gymnast’s body for 0.22 s.
    In the layout position, the gymnast’s moment of inertia is 11.4 kg-m2

    What is her angular acceleration and her final angular velocity (during layout position)?


    Heres what i got

    Angular acceleration
    T=Iα

    115 Nm=11.4 kg-m2(α)
    115 Nm/11.4 kg-m2 = 11.4 kg-m2(α)/ 11.4 kg-m2 =10.08 kg-m2

    Angular velocity (w)
    Tt=I(w)

    104 Nm (.22s) = 11.4kg-m2(w)
    104Nm(.22s) / 11.4kg-m2 = 11.4kg-m2(w) / 11.4kg-m2 = 2.22 kg-m2
     
  2. jcsd
  3. Jun 19, 2004 #2

    arildno

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    You seem to know which equations you should use, but you must develop a clearer notation:
    "115 Nm=11.4 kg-m2(α)
    115 Nm/11.4 kg-m2 = 11.4 kg-m2(α)/ 11.4 kg-m2"

    Your second line equaltiy is certainly consistent with your first line equality; i.e, your doing correct maths.

    However, when writing units, "kg-m2" is very cryptic; write instead kg*m^2
    (Or:[tex]kg*m^{2}[/tex])

    Your continued equality has wrong units, apart from being a very unfortunate way of notation:

    We know that:[tex]Nm=\frac{kg*m^{2}}{s^{2}}[/tex]
    Hence:[tex]\frac{Nm}{kg*m^{2}}=\frac{1}{s^{2}}[/tex]
    Surely, this is the unit of angular acceleration!
    In order to make a clearer notation, this is an example:
    [tex]115Nm=11.4kg*m^{2}\alpha[/tex]
    [tex]\alpha=\frac{115}{11.4}\frac{Nm}{kg*m^{2}}=10.08s^{-2}[/tex]

    Why have you suddenly changed 115 into 104 in your equation for the angular velocity?
    You end up with wrong units again, and you must work on your notations.
     
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