BOX 7.3 Qualitative Strategies Written by Students Students enrolled in an introductory physics course were asked to write a strategy for an exam problem Exam Problem: A disk of mass, M = 2 kg, and radius, R = 0.4 m, has string wound around it and is free to rotate about an axle through its center. A block of mass, M = 1 kg, is attached to the end of the string, and the system is released from rest with no slack in the string. What is the speed of the block after it has fallen a distance, d = 0.5 m. Don't forget to provide both a strategy and a solution. Strategy 1: Use the conservation of energy since the only nonconservative force in the system is the tension in the rope attached to the mass M and wound around the disk (assuming there is no friction between the axle and the disk, and the mass M and the air), and the work done by the tension to the disk and the mass cancel each other out. First, set up a coordinate system so the potential energy of the system at the start can be determined. There will be no kinetic energy at the start since it starts at rest. Therefore the potential energy is all the initial energy. Now set the initial energy equal to the final energy that is made up of the kinetic energy of the disk plus the mass M and any potential energy left in the system with respect to the chosen coordinate system. Strategy 2: I would use conservation of mechanical energy to solve this problem. The mass M has some potential energy while it is hanging there. When the block starts to accelerate downward the potential energy is transformed into rotational kinetic energy of the disk and kinetic energy of the falling mass. Equating the initial and final states and using the relationship between v and * the speed of M can be found. Mechanical energy is conserved even with the nonconservative tension force because the tension force is internal to the system (pulley, mass, rope). Strategy 3: In trying to find the speed of the block I would try to find angular momentum kinetic energy, use gravity. I would also use rotational kinematics and moment of inertia around the center of mass for the disk. Strategy 4: There will be a torque about the center of mass due to the weight of the block, M. The force pulling downward is mg. The moment of inertia about the axle is 1/2 MR2. The moment of inertia multiplied by the angular acceleration. By plugging these values into a kinematic expression, the angular speed can be calculated. Then, the angular speed times the radius gives you the velocity of the block.      The first two strategies display an excellent understanding of the principles, justification, and procedures that could be used to solve the problem (the what, why, and how for solving the problem). The last two strategies are largely a shopping list of physics terms or equations that were covered in the course, but the students are not able to articulate why or how they apply to the problem under consideration.      Having students write strategies (after modeling strategy writing for them and providing suitable scaffolding to ensure progress) provides an excellent formative assessment tool for monitoring whether or not students are making the appropriate links between problem contexts, and the principles and procedures that could be applied to solve them (see Leonard et al., 1996).