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A light beam of frequency f hits a mirror of length 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.
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
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
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