Chapter 33, Problem 47AP

You are working at NASA, in a division that is studying the possibility of rotating small spacecraft using radiation pressure from the Sun. You have built a scale model of a spacecraft as shown in Figure P33.47. The central body is a spherical shell with mass m = 0.500 kg and radius R = 15.0 cm. The thin rod extending from each side of the sphere is of mass m_r = 50.0 g and of total length ℓ = 1.00 m. At each end of the rod arc circular plates of mass m_p = 10.0 g and radius r_p = 2.00 cm, with the center of each plate located at the end of the rod. One plate is perfectly reflecting and the other is perfectly absorbing. The initial configuration of this model is that it is at rest, mounted on a vertical axle with very low friction. To begin the simulation, you expose the model to sunlight of intensity I_s = 1 000 W/m², directed perpendicularly to the plates, for a time interval of Δt = 2.0 min. The sunlight is then removed from the model. Determine the angular velocity ω with which the model now rotates about the axle.

Figure P33.47