Wind a string around a yo-yo a couple of times. Holding the string horizontally, give it a gentle tug. Does the yo-yo roll away from you or towards you? Is it what you expected? Contrast this with holding the string vertically. What happens now?
This block, our physics class has been analyzing rotations and anomalous yo-yo behavior. We have been modeling increasingly sophisticated physical systems this year, culminating in rotation this block. Combining Newton’s laws with conservation of angular momentum, we now have the tools to tackle most physical problems involving low velocities and macroscopic dimensions.
Our studies of Newtonian mechanics of point particles and rigid bodies have led us to analyze the inverse square law of universal gravitation and Kepler’s laws of planetary motion. The students have explored satellite motion, the physics of sandwich sharing between astronauts in orbit, and questions about throwing a ball parallel to the ground on an airless, non-spinning earth.
Our final weeks of the block have focused on projecting a light on uniform circular motion, and analyzing the shadowy motion, so to speak. In the process, we have stumbled across the ideal spring, which obeys Hooke’s law and undergoes sinusoidal oscillations in time. We have generalized this motion to pendulums undergoing small amplitude oscillations, tried our first approximation technique, and worked on powerful problem-solving methods applying the general physical conservation principles of energy and momentum.
On the pedagogical front, we have adopted an online forum for students to discuss homework, offer hints, and comment on other students' ideas. There has been much activity and humor in the online discussions, and students are able to answer each other’s questions, clarifying doubts and sharing their own observations outside of class. The questions on their homework now bear tags that help them make connections to what they have learned before and reflect on their thinking as they ponder a problem. In some homework, the students themselves tag the questions, and they will get more of an opportunity to do so in the future. As we move forward, this will help the students understand the context of the questions and their relationship to the class activities, and consolidate overarching physical principles we are studying.
-- Kaushik Basu