(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two square reflectors, each 1.00 cm on a side and of mass 4.00 g, are located at opposite ends of a thin, extremely light, 1.00-m rod that can rotate without friction and in a vacuum about an axle perpendicular to it through its center (the figure ). These reflectors are small enough to be treated as point masses in moment-of-inertia calculations. Both reflectors are illuminated on one face by a sinusoidal light wave having an electric field of amplitude 1.15 N/C that falls uniformly on both surfaces and always strikes them perpendicular to the plane of their surfaces. One reflector is covered with a perfectly absorbing coating, and the other is covered with a perfectly reflecting coating.

2. Relevant equations

Near as I can tell:

E_{max}= cB_{max}

P_{rad}for Perfect absorbtion = Intensity/c

P_{rad}for Perfect reflection = 2*Intensity/c

P_{rad}= F/Area

Intensity = (E_{max}* B_{max})/(2μ_{o})

Moment of Inertia for Rod = (mL^{2})/12

Parallel Axis Theorem: I_{cm}=I + md^{2}

Angular acceleration α = ω^{2}r

Angular frequency ω^{2}= mgd/Inertia

3. The attempt at a solution

I calculated B_{max}and used 4πx10^-7 for μ_{o}to get the Intensity of the light. Considering the light is hitting both cubes, both receive a Radiation Pressure corresponding to whether they absorb the waves or reflect them. I assume the forces on the areas will cancel to some degree, leaving a Radiation Pressure of I/c on the right cube (that one looks like it is supposed to be the reflecting cube). Trying to yield an acceleration by using the equation a = I(A)/mc (since pressure is force/area), where m is the mass of both cubes gives me horribly large and horribly wrong results.

The moment of inertia for a rod is normally (mL^{2})/12, but the question claims the rod is "extremely light", which I seem to notice usually means the rod has negligable mass. I resort to the Parallel Axis theorem to solve for the moment of inertia of this magic device, which would mean I_{cm}= 2md^{2}, since both cubes are of equal masses and equal distance from the pivot point of the rod. Substituting in for mgd/Inertia to get ω^{2}and multiplying by r to get α yields incorrect results.

I suppose what I'm asking is whether I'm on the right track (which doesn't seem likely, considering my results being so unrealistic) and what I should consider when facing an equation where "m" is needed, as I'm a bit confused as to whether I should be using the mass of both cubes or the mass of only one.

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# Homework Help: Angular Acceleration due to Light Waves

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