PROBLEMS FROM SERWAY - CHAPTER 11
        
        
         6.  The angular position of a point on a wheel can be
             described by theta = 5 + 10t + 2t^2 rad.  Determine
             the angular position, speed, and acceleration of the
             point at t = 0 and t = 3 s.
        
         7.  A car accelerates uniformly from rest and reaches a
             speed of 22 m/s in 9 s.  The diameter of a tire is 58
             cm.  (a) Find the number of revolutions that a tire
             makes during this motion, assuming no slipping occurs.
             (b) What is the final rotational speed of a tire, in
             revolutions per second?
        
        27.  A particle is located at the vector position
             r = (i + 3j) m, and the force acting on it is
             F = (3i + 2j) N.  (r,F,i, and j are vectors.)
             What is the torque about (a) the origin and (b)
             the point having coordinates (0,6) m.

        58.  Two astronauts, each having a mass of 75 kg, are
             connected by a 10-m rope of negligible mass.  They
             are isolated in space, orbiting their center of mass
             at speeds of 5 m/s. (a) Calculate the magnitude of 
             the angular momentum of the system by treating the
             astronauts as particles. (b) Calculate the kinetic
             energy of the system.  By pulling in on the rope,
             the astronauts shorten the distance between them to
             5 m. (c) What is the new angular momentum of the
             system?  (d) What are the astronauts' new speeds?
             (e) What is the new kinetic energy of the system?
             (f) How much work is done by the astronauts in
             shortening the rope?

        65.  An electric motor can accelerate a Ferris wheel of 
             moment of inertia I = 20000 kg m^2 from rest to 10
             rev/min in 12 s.  When the motor is turned off, the
             Ferris wheel slows down from 10 to 8 rev/min in 10 s,
             due to frictional losses.  Determine (a) the torque
             generated by the motor to bring the wheel to 10
             rev/min and (b) the power needed to maintain the
             Ferris wheel's rotation speed of 10 rev/min.