Two square reflectors, each 2.25 cm on a side and of mass 4.25 g, are located at

Question

Two square reflectors, each 2.25 cm on a side and of mass 4.25 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 (see figure below). 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 1.50 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. What is the angular acceleration of this device?

Explanation / Answer

moment of inertia about centre= 2* m(l/2)2

=2*4.25*10^-3*(.5)2

=2.125*10-3 Kgm2

force on reflector = 2*(0.637*1.50)*(2.25*10-2)2 into the plane E av=Epk x 0.637

=9.67*10-4 N

FORCe on absorber=(0.637*1.50)*(2.25*10-2)2 =4.84*10-4 N into the plane

so net torque=   (0.637*1.50)*(2.25*10-2)2 x 0.5 = 4.84*10-4 x 0.5 = 2.42*10-4 Nm

so angular accln= torque/moment of inertia= ( 2.42*10-4)/ (2.125*10-3)

=0.114 rad/s2

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