Problem 37P

A typical white-dwarf star, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?

Solution 37P Here we consider to emphasize that we adding the two given torques. The 12 N force is producing positive torque because it is in counterclockwise direction and 10 N force is producing negative torque because it is in clockwise direction.for each torque r is 0.30 m. Assume that the rope comes off tangent to the pulley on each side so that angle will be = 90 ,sin(90 ) = 1 2 The moment of inertia of cylinder is given by I =½ MR 2 I =½ (0.80 kg)(0.30 m) I = 0.036 kg/m 2 Angular acceleration of pulley is given by = /I 2 = (0.30 m)(12 N)(0.30 m)(10 N)/(0.036 kg/m ) = (0.30 m)(12 N 10 N)/(0.036 kg/m ) 2 = 17 rad/s 2 The specific angles the rope make with vertical do not matter,as long as they are exerting torques in opposite directions and coming off the pulley tangentially.