Torque, Momentum and Reflection

AI Thread Summary
The discussion focuses on calculating the angular acceleration of a rotating mirror struck by a light beam. The moment of inertia of the mirror is determined as I = ML²/3, while the linear momentum of the light beam is expressed as p = hf/c. The force exerted on the mirror is derived from the variation of linear momentum, leading to the equation F = 2Nhf/c. The torque on the mirror is calculated using the force and the distance from the pivot point, resulting in the equation T = (3/2) NhfL/c. The final expression for angular acceleration γ is derived as γ = (9/2) Nhf/McL, confirming the calculations are largely correct.
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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
 
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The linear momentum of the beam is p = hf/c
You mean photon, not beam, but otherwise looks ok.
 

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