Problem 32.39 Constant? PartA Two square reflectors, each 1.00 cm on a side and

Question

Problem 32.39 Constant? PartA 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 (Figure 1 These reflectors are small enough to be treated as point masses in moment-of-inertia calculations. Both raflectors 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 aurfaces. One reflector ia covered with a perfectly absorbing coating, and the other is covered with a perfectly reflecting coating. What is the angular acceleration of this device? anure 1. Theon.bng ele rad/s Submit Request Answer

Explanation / Answer

The time-averaged intensity of a plane polarized wave is

<I> = 1/2 eps0 c E^2,

where E is the amplitude of the electric field of the wave.

The pressure exerted by the wave is given by

p= <I> / c when absorbed

p = 2 <I> / c when reflected.

The torque on the apparatus therefore is

T = 2<I>/c * A * R - <I>/c * A * R = <I>/c *A * R

The moment of inertia is mR^2 + mR^2 = 2mR^2.

Therefore the angular acceleration is

dw/dt = T/(2mR^2)

= <I> A R /(2 m c R^2)

= 1/2 eps0 c E^2 A /(2 m c R)

= eps0 E^2 A /(4m R)

Here that gives

dw/dt = (8.85*10^-12)* (1.15)^2 *(1.00*10^-2 m)^2 / (4 * 4.00*10^-3kg * 0.50m)

= 1.464*10^-13 rad/s^2

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