EXAM 3                    December 1, 1989                PS 207   

  If you need a constant not given here or do not understand a problem,  
please ask me about it.  Remember to include diagrams and explain your  
reasoning.  No notes, books, etc. may be used during this exam.  
               2
  g = 9.8 m/sec   
                                       -31
  The mass of the electron is 9.11 x 10    kg  

  1.  Explain how, knowing 

                             1    2
              x = x  + v t + - a t , 
                   0    0    2                   

                          you can determine both of the equations governing

motion under constant torque.  Be sure to state explicitly the relations  

you use between linear variables and angular variables.  


  2.  (From homework)  A bullet of mass  m  strikes a ballistic  

pendulum of mass  M .  The center of mass of the pendulum rises a  

vertical distance  h .  Assuming that the bullet remains embedded in

the pendulum, calculate the initial speed of the bullet.  


  3.  A uniform stick of mass  M  and length  L  is suspended

horizontally with one end on the edge of a table and the other end

held by hand.  The second end is suddenly released.  Calculate, at

the instant after release, the angular acceleration around the end

on the table, the vertical acceleration of the center of mass, and

the force exerted upward on the stick by the table.  


  4.  The front and rear wheels of an automobile are separated by a  

distance  d , and the center of mass is a height  h  above the ground.   

Suppose that the automobile has rear-wheel drive and is accelerating  

along a level road at a rate  a .  When the automobile is parked, half  

its weight is supported by the front wheels.  Find the normal forces on  

the front and rear wheels when the car is accelerating, pretending that  

the body remains horizontal despite the acceleration.  [NOTE: because of  

the acceleration, if you take torques around an axis attached explicitly  

or implicitly to the car, that axis MUST pass through the center of mass  

of the car, or your equations will be incorrect.]