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:

Physics quiz question: ice skater angular momentum conservation

Physics 5A Quiz 5, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 8.78

[3.0 points.] A figure skater is spinning at a rate of 2.00 rev/s with his arms pulled into his chest. He then extends his arms outwards, increasing his rotational inertia to 150% of its original value. What is the magnitude of his new rate of rotation?
(A) 0.67 rev/s.
(B) 0.89 rev/s.
(C) 1.3 rev/s.
(D) 1.5 rev/s.

Correct answer: (C)

Assume that there are no external torques, or that this process takes a sufficiently short time such that angular momentum is conserved. Then:

L_i = L_f,

I_i*w_i = I_f*w_f,

where 1.5*I_i = I_f. Thus w_f = (I_i/I_f)*w_i = (1/1.5)*w_i.

Student responses
Sections 0906, 0907
(A) : 3 students
(B) : 6 students
(C) : 23 students
(D) : 7 students

Physics quiz question: ring and disk

Physics 8A Quiz 9, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q9.4

[3.0 points.] Consider a disk that rotates about a fixed vertical axis at a rate of 2.00 rad/s. The diameter of the disk is D, and its mass is M. A stationary thin, uniform ring with the same diameter and mass as the disk is dropped straight down onto the disk. The ring and disk reach a new final angular speed as they rotate together. Neglect angular impulses due to torques exerted by external friction and drag forces during this brief process.

Which one of the following choices best describes the quantities that were conserved during this process?
(A) Both angular momentum and rotational kinetic energy were conserved.
(B) Only angular momentum was conserved.
(C) Only rotational kinetic energy was conserved.
(D) Neither angular momentum nor rotational kinetic energy was conserved.

(Cf. Young and Freeman, University Physics, 11/e, Problem 10.43.)

Correct answer: (B)
No external angular impulses are exerted on this system, so the total angular momentum of the system is conserved. However, friction allows the disk to speed up the ring such that they rotate together with the same final angular speed, thus rotational kinetic energy is lost for this completely inelastic "angular collision." (The change in the total rotational kinetic energy during this process can be shown to be negative, once w_f is determined from applying angular momentum conservation.)

Student responses:
(A) : 9 students
(B) : 12 students
(C) : 6 students
(D) : 3 students

Partially inelastic angular collision

kill sponge bob
Originally uploaded by bryan stupar.

Physics 8A learning goal Q9.5

Transfer of angular impulse to stationary SpongeBob SquarePants.

http://www.flickr.com/photos/bryanstupar/131858646/in/pool-slocounty/