Physics midterm problem: inelastic rotational collision

Physics 205A Midterm 2, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 8.76

[20 points.] A 0.500 kg point mass is dropped onto a disk rotating at 4.00 rad/s that has a mass of 0.700 kg and a radius of 0.150 m. The point mass eventually rotates with the disk at a distance of 0.100 m from the axis. What is the final kinetic energy of the disk and point mass system? Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Applies conservation of angular momentum to find the final angular velocity of the disk and point mass system; and then calculates the change in initial and final rotational kinetic energies in this inelastic rotational collision.
  
• r = 16/20:
  Nearly correct, but includes minor math errors.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Some attempt at applying conservation of angular momentum before evaluating the final kinetic energy.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Applies kinetic energy conservation to find final rotational kinetic energy, even though this is an inelastic rotational collision (as seen in lab), and if it were elastic, the final rotational kinetic energy would be exactly equal to the initial kinetic energy.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Sections 70854, 70855
p: 1 student
r: 3 students
t: 3 students
v: 31 students
x: 3 students
y: 0 students
z: 2 students

A sample of the sole "p" response, applying angular momentum conservation to find the final angular velocity of the point mass and disk system, and then calculating the final (rotational) kinetic energy of this system (from student 0215):
A sample "t" response (from student 0420), with an attmempt to calculate the final kinetic energy of the system, but with a realization that the final angular velocity is not yet determined: