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Torque, Momentum and Reflection

  1. Jun 2, 2013 #1
    A light beam of frequency f hits a mirror of lenght L at a distance 3/4 L from one end, which is fixed but can rotate freely around the axis as shown. The mirror has mass m and can be considered a rectangular plate. The light beam hits (and fully reflects) the mirror at a rate of N photons per second. Find the angular acceleration of the mirror.
    [Broken]

    I did this, can anyone tell me if it's right?

    The moment of inertia of the mirror is I = ML²/3
    The linear momentum of the beam is p = hf/c

    The variation of the linear momentum in function of time is 2Nhf/c = F (where F is the force exerted on the mirror)

    The torque T = F.(3/4L) = (3/2) NhfL/c = Iγ = (ML²/3) γ
    γ = (9/2) Nhf/McL
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jun 3, 2013 #2

    haruspex

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    You mean photon, not beam, but otherwise looks ok.
     
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