The cross diagram is a way to illustrate and plan the solutions for all kinds of constant-acceleration kinematics problems--including projectile motion, multistage, and multiple-object problems. The cross diagram arranges the kinematic variables in a logical way, making the kinematic relationships between them easy to identify. Combined with a…

Collisions are real-world situations from everyday life (such as car crashes, playing billiards, etc.) that can be described and understood by the principle of conservation of momentum. One might expect that learning from simple collisions might help students understand more complicated physical phenomena. However, from our teaching experiences we…

Before students learn Kirchhoff's rules, they are typically taught how to solve "combined series-parallel" circuits. The method presented in many textbooks begins by drawing a series of simplified circuits, replacing series and/or parallel elements with their equivalent resistances, eventually reducing the circuit to a voltage source and…

Nearly all physics instructors recognize the instructional value of force diagrams, and this journal has published several collections of exercises to improve student skill in this area. Yet some instructors worry that too few students perceive the conceptual and problem-solving utility of force diagrams, and over recent years a rich variety of…

Two computer-generated star charts that can be used as overlay transparencies to show an expanding universe are presented. Directions on how to use the star charts to determine the Hubble constant and the age of the universe are provided. (KR)