A unform circular disk of mass m = 24.0 g and radius r = 40.0 cm hangs verticall

Question

A unform circular disk of mass m = 24.0 g and radius r = 40.0 cm hangs vertically from a fixed, frictionless, horizontal hinge at a point on its circumference as shown in Figure P34.39a. A beam of electromagnetic radiation with intensity 10.0 MW/m^2 is incident on the disk in a direction perpendicular to its surface. The disk is perfectly absorbing, and the resulting radiation pressure makes the disk rotate. Assuming the radiation is always perpendicular to the surface of the disk, find the angle theta through which the disk rotates from the vertical as it reaches its new equilibrium position shown in Figure 34.39b.

Explanation / Answer

Radiation pressure P is given by

P = Radiation intensity/speed of light

= (10.0*10^6)/(3*10^8)

= 0.03333 Pa

Force on disc = P*area

= 0.03333*pi*0.4^2

= 0.016755 N

Centre of mass is at the centre of disc, at which gravitational force act

mg*sin(theta) = 0.016755

0.024*9.81*sin(theta) = 0.016755

sin(theta) = 0.07116

theta = 4.08 degrees

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