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
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