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How do you add angular momentum in different dimensions?

  1. Aug 10, 2015 #1
    Say a ring is spining around the z-axis, an angular impulse is then applied to it in the x-axis, what is the resultant motion qualitatively and quantitatively? How can it be calculated?

    (You can make up the quantity of z-angular momentum and x-angular impulse)
  2. jcsd
  3. Aug 10, 2015 #2
    I assume you mean that the impulse is delivered when the ring is perfectly in the x-z plane. Initially the ring has angular momentum [itex] \vec{L} = \omega_z\hat{z} [/itex], and the impulse introduces some angular momentum [itex] \omega_x\hat{x} [/itex]. The total angular momentum will then be the vector sum of these:

    [itex] \vec{L'} = (\omega_x, 0, \omega_z) [/itex], and given the rotational symmetry of the ring, it will start to rotate about an axis parallel to this new vector, which now lies in the x-z plane. If the ring is spinning on a table, for example, then there is the additional complication of torque on the ring due to gravity, and it will precess about this axis.
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