A uniform circular disk of mass m = 22.6 g and radius r = 44.0 cm hangs vertical

Question

A uniform circular disk of mass m = 22.6 g and radius r = 44.0 cm hangs vertically from a fixed, frictionless, horizontal hinge at a point on its circumference as shown in Figure a. A beam of electromagnetic radiation with intensity 10.3 MW/m2 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 ?through which the disk rotates from the vertical as it reaches its new equilibrium position shown in Figure b.

Explanation / Answer

Radiation pressure P is given by

P = Radiation intensity/speed of light

= (10.3*10^6)/(3*10^8)

= 0.03433 Pa

Force on disc = P*area

= 0.03433*pi*0.44^2

= 0.0208 N

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

mg*sin(theta) = 0.0208

0.0226*9.81*sin(theta) = 0.0208

sin(theta) = 0.0938

theta = 5.38 degrees

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