Physics with Trigonometry

Physics with Trig is intended for students with sufficient math skill to allow for advanced critical thinking in a mathematical frame work. By requiring students to be in Advanced Algebra II or above, the content can address complex systems without having students overwhelmed by the mathematical expectations. While there are algebraic frameworks, students are encouraged to test new theories and ideas in the real world while allowing them to back up their theories with mathematics. PWT is divided into three mods: Forces and Motion, Circles and Conservation and Waves and Optics.

Forces and Motion

All students are required to take Forces and Motion first, because all of Mechanics requires a strong background in how and why things move. When discussing kinematics, students apply the topics to the physical world. We address problems and applications that span a wide variety of real world situations - in 1D Kinematics, students explore the practical relationship between speed and stopping distance and how that applies to their own driving choices. In two-dimensional motion, students decide how pilots should drop aid from moving aircraft to best serve those below.

Forces require students to think about their choices, from exactly how much does a wet road impair stopping in a car to how to kick a soccer ball to score that final goal. They use real like lab interactions to test their theories and simulations to explore within the constraints of an idealized world. They explore campus using vectors and use toys and whiteboards to express scientific concepts. This course serves as a prerequisite for those intending AP.

Circles and Conservation

Once they’ve tackled the linear world, students are ready to explore other models of the world. By using flying pigs, students can predict the forces and a string and even verify what they know about gravity. In a discussion of energy, student can see how heat and motion are related, and figure out how toys and cars and people can move. In momentum, collisions become real, allowing students to quantify what really happens when an airbag deploys, and what that means for the human body.

This mod culminates with a comprehensive project allowing students to explore the safety features of the cars they drive. They will use their research on seat belts, crumple zones and air bags to create a safe driving experience for an egg. In addition, they will create a highway safety commerical to encourage others to make good driving choices. This brings together everything they’ve learned in the first two mods of physics. Right now, teenagers are the least likely driving groups to wear seat belts - by studying the physics, they can see first hand how that simple act might save their lives.

Waves and optics

In a departure from classical mechanics, this mod allows students to explore a more artistic view of the world. We talk about pendulums and motion on swings, discussing the ideal time in the motion to push a friend for maximum height and how clocks can keep perfect time - relating the ideas of mass and force and kinematics to periodic motion. We show how all those motions are related and predictable, and how what they have studied in trig applies to the real world.

We spend most of the mod, however, talking about light and sound. Students can learn practical information about lenses and mirrors, and how light sometimes behaving like the ocean and other times like a baseball. We explore corrective lenses for eyes and what they do, and student learn to mix color and light with beautiful results. We apply sound to music, so that student understand how to tune a guitar while exploring how the human ear interprets music. They create a musical wind chime that plays their favorite musical chord and a telescope to explore the sky. Mostly, it gives students tools to describe how they see the world they live in and the cosmos beyond.

AP Physics C: Mechanics

For those student bitten by the Physics bug, AP Physics C is a great way to take a deep dive into the mathematical and physical background of the topics addressed in PWT while gaining college credit. This calculus based course shows the why of math instead of just memorizing. While this course moves at an advanced pace, it is structured around the lab experience instead of including lab as an afterthought.

The course is organized around experiments rather than physics topics. Each experiment incorporates several aspects of physics, so students don’t see them as isolated examples of particular concepts. The course has a hands-on laboratory component covering an array of experiments. Instead, students learn to look at a physical situation and see how it involves principles of dynamics, kinematics, energy, etc.

Although this is not the best way to introduce a new powerful concept, such as energy conservation, our students are already familiar with the basic tools of physics. We don’t want to simplify our experiments to highlight a particular concept to make it clear.  Instead, we want our students to deepen their understanding and be able to pick out familiar concepts from more complicated (and realistic) situations. Early in the course, we use experiments to introduce new topics, such as air resistance and rotation. After seeing new phenomena in the lab, there is motivation to explore them in class through demonstrations and theory. 

Since each experiment involves several aspects of physics, our classroom discussions and homework assignments must mirror that spiraling approach. For example, we never have a unit or a test that covers energy specifically. Instead, we cover bits and pieces of energy when appropriate. Eventually, students are able to handle any problem involving energy. What is more important is that they learn to recognize how energy is involved in any situation and that they learn when it is the best approach to solving a problem.

After this course, students can confidently leave with a strong foundation in Physics.