Sample test 3, rotations and angular momentum
Nov, 2001
General Physics I

        Table of moment of inertia (in case you need it)
        I disk = 1/2 M R^2
        I sphere = 2/5 M R^2
        I rod, center = 1/12 M L^2  , where L = total length of the rod
        I rod, end   = 1/3 M L^2

1)    Two balls, one massing 1 kg, and the other massing 2 kg, are
      connected by a 2 meter string.  (The string’s mass is
      negligable.)  The objects are out i space, far from any
      gravitational forces or other influences.  The balls are turning
      about their center of mass at a rate of 3 revolutions per
      second.

      (a) Where is the center of the mass of this system?
      (b) Find the  moment of inertia.  
      
      (c) Find the kinetic energy of the system in two different ways
           and show that they are equal:

              A. Using the angular rotation speed and the total moment
              of inertia, and

              B. Using the tangential speed of each ball, and adding
              their tangential (linear) kinetic energies.

(2)   A flywheel (i.e. solid disk) masses 3 kg and has a radius of 0.25m
      Suppose it has a handle attached to the axle with a lever
      arm of 1 meter, and you push on the end of the handle with a
      force of 10 Newtons for 10 seconds.  (a) How much torque are you
      applying?  (b) What is the angular acceleration of the disk?
      (c) How fast is the disk turning at the end of the 10 seconds?

(3)   A star spins around in about a week.  Suppose its hyrdrogen fuel
      runs out, and it shrinks into a white dwarf without losing any
      mass.  How long does it take to rotate after it shrinks?
      (R_star = 10^5 km , R_whitedwarf = 5 10^3 km).  Explain what
      physics principles you are using to reach a solution.


(4)   In class we set up the equations of motion for a rotating object
      rolling down an inclined ramp, solving the equations of linear
      and angular motion simultaneously.  Set up those equations,
      including all the forces, and solve them to find the
      acceleration of a sphere down a ramp inclined at 45 degrees.