Deep Physics: Mechanics of Motion for Talented High Schoolers
Real mechanics of motion, taught from kinematics through Newton’s laws, conservation of energy and momentum, and universal gravitation. For talented high schoolers.
Online for homeschool families anywhere · or in-person in Princeton, NJ
A World Through the Lens of Mechanics of Motion
Mechanics is the oldest subject in physics, and still its foundation. From a thrown ball to a planet’s orbit, the same handful of laws governs every motion in the everyday world.
Throw a ball across a room. Its path is a parabola, every time. The same equations that describe the ball describe a planet around the Sun.
Two ice skaters of different weights push off from each other. Both move apart. The lighter one moves faster. The product of mass and velocity is equal and opposite on the two sides, before and after.
A pendulum at the bottom of its swing has all kinetic energy and no potential. At the top, all potential and no kinetic. The total never changes across the swing.
Apollo 15, 1971. An astronaut drops a hammer and a feather on the surface of the Moon, on live television. They hit the ground together.
Three short laws and three conservation principles describe every one of these. Newton’s framework, together with conservation of energy, momentum, and angular momentum, predicts the motion of every object in the everyday world. From a thrown ball to a planetary orbit, the same equations apply.
You will:
- Predict the trajectory of any projectile from initial conditions and gravity alone.
- Apply Newton’s three laws to set up and solve the equation of motion for any system of forces.
- Use conservation of energy and momentum to solve problems faster than by tracking forces directly.
- Derive Kepler’s three laws of planetary motion from Newton’s law of universal gravitation.
What You Will Actually Understand
1. Kinematics: Describing Motion
Position, velocity, and acceleration, before any talk of forces. Motion in one and two dimensions. Average and instantaneous velocity, acceleration, the constant-acceleration formulas. Projectile motion as two independent one-dimensional problems happening at the same time.
2. Newton’s Laws of Motion
Force, mass, and acceleration as a single equation. Newton’s three laws and what each one says. Forces as vectors. Inertial frames of reference. Friction, tension, normal force. Free-body diagrams as the universal tool for setting up any mechanics problem.
3. Energy and Work
A second way of looking at every problem in mechanics. Work done by a force. Kinetic energy and the work–energy theorem. Potential energy for gravity and springs. Conservation of energy and what it lets you skip when you use it well.
4. Momentum and Collisions
What survives a collision, and what does not. Linear momentum and impulse. Conservation of momentum for any closed system. Elastic and inelastic collisions in one and two dimensions. Center of mass and how it simplifies the problem. Reactive (rocket) motion: momentum conservation when mass is ejected.
5. Circular Motion and Universal Gravitation
From a stone on a string to the orbit of the Earth. Uniform circular motion: centripetal acceleration and the force that supplies it. Newton’s law of universal gravitation. Orbits, the three cosmic velocities (orbital, escape, and solar escape), and Kepler’s three laws of planetary motion.
6. Frames of Reference
How the same motion looks different from a moving observer. Galilean relativity. Velocity addition between inertial frames. Non-inertial frames and the apparent forces, such as centrifugal and Coriolis, that they introduce. Why physics keeps the same form in any inertial frame.
The specific topics, and the depth given to each, may shift depending on class priorities and the dynamics of the cohort.
Schedule, Pricing & Enrollment
Formats: Fall, Spring, and Summer semesters.
Schedule, format, tuition, refund policy, and certificates apply to every Lyceum course. They live on the Physics Lyceum: High School overview.
To enroll, schedule a call. We confirm fit, prerequisites, and the right semester.
Part of the SoTS Physics Lyceum
Mechanics of Motion is one of six classical core courses in the SoTS Physics Lyceum: a multi-year curriculum in Princeton, NJ. Students earning the Mastery in Classical and Modern Physics complete the six classical core courses plus any two of the four modern electives.
Classical core: Mechanics of motion. Mechanics of bodies and fluids. Waves and oscillations. Thermodynamics. Electricity and magnetism. Geometric optics.
Modern electives: Special Relativity. Quantum mechanics. Nuclear and particle physics. Astronomy and cosmology.
The Lyceum is built on the Deep Physics methodology.