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Introductory Physics Homework Help
Angular Acceleration due to Light Waves
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[QUOTE="JackFlash, post: 3593671, member: 368559"] [h2]Homework Statement [/h2] 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. [ATTACH=full]147154[/ATTACH] [h2]Homework Equations[/h2] Near as I can tell: E[SUB]max[/SUB] = cB[SUB]max[/SUB] P[SUB]rad[/SUB] for Perfect absorbtion = Intensity/c P[SUB]rad[/SUB] for Perfect reflection = 2*Intensity/c P[SUB]rad[/SUB] = F/Area Intensity = (E[SUB]max[/SUB] * B[SUB]max[/SUB])/(2μ[SUB]o[/SUB]) Moment of Inertia for Rod = (mL[SUP]2[/SUP])/12 Parallel Axis Theorem: I[SUB]cm[/SUB]=I + md[SUP]2[/SUP] Angular acceleration α = ω[SUP]2[/SUP]r Angular frequency ω[SUP]2[/SUP] = mgd/Inertia [h2]The Attempt at a Solution[/h2] I calculated B[SUB]max[/SUB] and used 4πx10^-7 for μ[SUB]o[/SUB] 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[SUP]2[/SUP])/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[SUB]cm[/SUB]= 2md[SUP]2[/SUP], 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[SUP]2[/SUP] 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. [/QUOTE]
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Angular Acceleration due to Light Waves
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