Question 1. In tutorial, you observed the following three experiments involving a student sitting at rest on a stool, holding a spinning bicycle wheel as shown at right:
Experiment I: The student places his arm against the side of the wheel, slowing it to half its initial angular speed.
Experiment 2: The student places his arm against the side of the wheel, bringing it to a stop.
Experiment 3: The student quickly flips the wheel over (so that it is spinning clockwise when viewed from above, with the same angular speed it had initially).
a. You observed that the final angular speed of the student in experiment 3 is greater than that in experiment 2. Account for this result using the ideas developed in the tutorial.
b. Rank the experiments according to final kinetic energy of the wheel, from largest to smallest. If the final kinetic energy of the wheel is the same in any two experiments, state so explicitly. (Hint: Can kinetic energy ever be negative?) Explain.
c. Rank the experiments according to final kinetic energy of the student, from largest to smallest. If the final kinetic energy of the student is the same in any two experiments, state so explicitly. Explain.
d. Rank the following four quantities from largest to smallest: the initial kinetic energy of the wheel (Kwi) and the final kinetic energy of the student-wheel system in experiments 1,2, and 3 (Ks1f, etc.). Explain. (Hint: It may be helpful to think about changes in energy other than mechanical energy.)
Question 2. The diagram below illustrates four hypothetical collisions that take place on a level, frictionless surface. The collisions are shown from a top-view perspective. All pucks are identical. If a linear or angular velocity is not specified, it is zero. If distances appear to be equal, assume that they are.
For each hypothetical collision:
a. Specify the direction of the angular momentum of the rod-puck(s) system with respect to the center of the rod both before and after the collision. If necessary, use the convention that a vector into the page is represented by the symbol ⊗ and a vector out of the page is represented by the symbol ?.
b. Specify the direction of the linear momentum of the rod-puck(s) system, both before and after the collision.
c. On the basis of your answers above, state whether each hypothetical collision could or could not occur. If a particular hypothetical collision could not occur, state whether it violates (I) the principle of conservation of linear momentum, (2) the principle of conservation of angular momentum, or (3) both.
