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The angular momentum of a flywheel

  1. Nov 20, 2007 #1
    The angular momentum of a flywheel having a rotational inertia of 0.200 kg·m2 about its axis decreases from 3.00 to 1.800 kg·m2/s in 1.80 s.

    (a) What is the average torque acting on the flywheel about its central axis during this period?
    (b) Assuming a uniform angular acceleration, through what angle will the flywheel have turned?
    (c) How much work was done on the wheel?
    (d) What is the average power of the flywheel?

    Basically, all i need is how to find the initial angular velocity for part b. The rest of the variables i have solved for.
  2. jcsd
  3. Nov 20, 2007 #2


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    Homework Helper

    The angular momentum of a rigid object about a fixed axis is given by

    [tex]L = I\omega[/tex]

    where [tex]I[/tex] is its moment of inertia bout this axis and [tex]\omega[/tex] is its angular speed about the same axis.
  4. Nov 20, 2007 #3
    The rotational components and equations are analogous to linear ones.

    Equation of motion:

    (1) [tex]x=x_0+vt+\frac{1}{2}at^2[/tex]
    (2) [tex]v=v_0+at[/tex]
    (3) [tex]F=ma[/tex]
    (4) [tex]W=Fx[/tex]
    (5) [tex]P=Fv[/tex]
    (6) [tex]a(x-x_0)=\frac{1}{2}(v^2-v_0^2)[/tex]


    (1) [tex]\phi=\phi_0+\omega t+\frac{1}{2}\alpha t^2[/tex]
    (2) [tex]\omega=\omega_0+\alpha t[/tex]
    (3) [tex]\tau=I\alpha[/tex]
    (4) [tex]W=\tau \phi[/tex]
    (5) [tex]P=\tau \omega[/tex]
    (6) [tex]\alpha(\phi-\phi_0)=\frac{1}{2}(\omega^2-\omega_0^2)[/tex]

    So to find the average torque in part (a), find the deceleration using angular equation 2.

    Part (b), use 6.

    Part (c), use 4.

    Part (d), use 5.
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