Chapter 8, Problem 58P

A system consists of four boxes modeled as particles connected by very lightweight, stiff rods (see figure below). The system rotates around the z axis, which points out of the page. Each particle has a mass of 7.00 kg. The distances from the z axis to each particle are r1 = 48.0 cm, r2 = 24.0 cm, r3 = 19.0 cm, and r4 = 38.0 cm. Find the rotational inertia of the system around the z axis. _________ kg · m^2

A student sits on a freely rotating stool holding two dumbbells, each of mass 3.02 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 0.98 m from the axis of rotation and the student rotates with an angular speed of 0.745 rad/s. The moment of inertia of the student plus stool is 2.56 kg · m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.292 m from the rotation axis (Figure b). (a) Find the new angular speed of the student. rad/s(b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. Kbefore =  J Kafter =  J

A heavy swing door has a mass of  m = 8,000 kg,  a width  w = 1.0 m,  and a height  H = 3.9 m.  The door swings about a vertical axis passing through its center. The moment of inertia of this door about the vertical axis of rotation is given by  I =  1 12 mw2.   (a) You stand on one side and push at the outer edge of the door and perpendicular to the face of the door with a force of F = 12.0 N.  Your friend pushes on the other outer edge of the door from the opposite side with the same force. What is the net torque, in N · m, applied to the door?     (b)What is the angular acceleration of the door in rad/s?   (c) Now consider a heavy door, with the same mass and dimensions as the one in part (a), that swings about a vertical axis passing through one long edge as shown in the diagram below. The moment of inertia of the door about this new axis of rotation is given by I =  1 3 mw2,  where m is the mass and w is the width of the door. How much force, in Newtons, must you…