Sit on a rotating stool and stretch your legs out. Push off a table and get yourself rotating. Now pull your legs in. Why do you speed up? Now stretch your legs out again; what happens?
This block, our physics class has been busy unraveling the next level of complexity in motion, transitioning from linear motion to rotational motion. We have also been applying fundamental conservation laws to more general problems and learning about an entirely new conservation law—the conservation of angular momentum. This conservation is manifest in the rotating chair example above and has been motivated by linear motion through the use of translational and rotational analogies.
The use of analogy in the classroom is a powerful method for formulating new ideas. To take an example on the mathematical side, we have revisited the dot product between vectors and introduced a new product, the cross product, which brings us into a higher dimension. The use of this is ubiquitous in the analysis of rotational motion, and students have been making impossibly difficult arrangements with their hand as they learn the much-celebrated "right-hand rule."
We began the block by studying circular motion, and the students have learned a new way to interpret Newton’s second law of motion. They get to consider the left side as arising from physical forces, and the right side as describing the effects of these as embodied by the geometry, or the kinematics. As a result, they have overcome the common pitfall of considering centripetal, or center-seeking, forces as fundamental forces. In fact, they have referred to it purely by the effect, "centripetal acceleration", and they have also come to understand and revel at why such words as "centrifugal" have been banned in the class from Day 1!
Most teachers of physics agree that rotational dynamics tend to be the most challenging aspects of mechanics for high school students. We are approaching it with motivations in linear motion, and intuitively appealing to how easy or hard it is to turn objects, but we will corroborate this intuition with more detailed experiments soon. One such experiment, which is to demonstrate the independence of rotational and translational motion, known as Chasles' Theorem, will be done by photographing carpet sections thrown across the lab with strobes or LEDs. We'll also make use of projects that our middle school students are currently building and discover what they have learned by tinkering with strobe photography, then repurpose their constructions for a quantitative investigation.
-- Kaushik Basu