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How did they get this precession frequency of this gyroscope?

  1. Jul 23, 2013 #1
    To summarize:

    1. The solenoid is supplied with an AC voltage.

    2. Produces an AC magnetic field out of the page

    3. Exerts an AC magnetic force on the Nb-Plate that's placed just outside of one end of the solenoid

    4. There is a fluid circulating in the torus, with angular momentum L in the z-direction (out of the page)

    5. What is the torque exerted on L due to the oscillating Nb-plate which forces the torus to oscillate with it?

    Directions: ∅ (Left-right), θ (In-Out of page)

    264sv49.png

    ACGyro2.png

    I'm not sure how they got an extra θ0 term in their torque about ∅. I know in small oscillations, the magnitude of change in L is

    ΔL ≈ θ0L

    Alternatively, considering change within half a period = T/2:

    ΔL/Δt = 2θ0L/T = 2fθ0L

    which also doesn't match their expression..
     
  2. jcsd
  3. Jul 24, 2013 #2
    No response yet!

    Which extra θ0 term are you referring to because I do not see an extra.

    Also, are you not missing a pi term in
    ΔL/Δt = 2θ0L/T = 2fθ0L
     
  4. Jul 24, 2013 #3
    Yeah, I did it two ways. Both don't match the expression they have derived..
     
  5. Jul 24, 2013 #4
    I think I know their line of thought, correct me if I'm wrong:

    In time Δt, the vector (θ0L) moves through an angle Δ∅. Hence

    ΔL = (θ0L)Δ∅

    Taking limits of Δt → 0,

    dL/dt = (θ0)L(d∅/dt) = θ0
     
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