Deep Physics: Mechanics of Bodies and Fluids for Talented High Schoolers
Real mechanics for things that spin, balance, and flow. Rotational dynamics, statics, and hydrostatics. For talented high schoolers.
Online for homeschool families anywhere · or in-person in Princeton, NJ
A World Through the Lens of Mechanics of Bodies and Fluids
Most objects in the world are not point particles. They have shape, they spin, they balance, they hold or release fluids. The mechanics of rigid bodies and fluids handles all of it with one continuous theory.
A figure skater pulls in her arms during a spin and turns faster. No one pushes her. The same skater, the same total mass. Move that mass closer to the axis, and the spin rate climbs.
A boat made of steel floats. A coin made of the same steel sinks. The difference is in the water displaced, not in what either is made of.
Race a hollow cylinder and a solid cylinder of equal mass and radius down a ramp. The solid one wins, every time. Where the mass sits, not how much there is, decides the race.
Hold a garden hose, then squeeze your thumb partly over the end. The water shoots farther. Less opening, same flow, more speed. Pressure at the constriction drops in step.
Rotation, balance, and flow look like very different problems. They share one structure. Once you treat angular momentum like linear momentum, torque like force, and pressure like a force per area, the same conservation laws and the same equations of motion carry you through all of them.
You will:
- Compute the moment of inertia of any simple rigid body and use it to predict its rotational acceleration.
- Apply conservation of angular momentum to predict the rate of a spin before and after a change in configuration.
- Determine whether any structure built of rigid bodies is in static equilibrium.
- Use the continuity equation and Bernoulli’s principle to predict pressure and speed at any point in a steady flow.
What You Will Actually Understand
1. Rotational Kinematics
Position, velocity, and acceleration, for things that turn. Angular position, angular velocity, angular acceleration. The link between linear and angular quantities for a point on a rotating body. The constant-angular-acceleration formulas.
2. Rotational Dynamics
Newton’s laws, written for rotation. Torque as the rotational analog of force. Moment of inertia and how it depends on the distribution of mass. Newton’s second law for rotation. Angular momentum and the law of its conservation. Gyroscopes and precession: what happens when the axis of a spinning body itself starts to move.
3. Static Equilibrium and Elasticity
When forces and torques balance, and how real materials yield under load. The two conditions for static equilibrium. Center of mass and center of gravity. Hooke’s law and Young’s modulus: how real materials stretch, compress, and snap. Stability of structures, from bridges and beams to ladders and arches.
4. Rolling and Combined Motion
Translation and rotation happening at the same time. Rolling without slipping. The constraint between translation and rotation. Kinetic energy of a rolling body. Why a hollow cylinder rolls more slowly than a solid one of equal mass.
5. Fluids at Rest: Pressure, Buoyancy, Surface Tension
Why a boat floats, a fish is not crushed at depth, and water climbs a thin tube. Pressure, density, and the hydrostatic pressure equation. Pascal’s principle. Buoyancy and Archimedes’ principle. Surface tension and capillarity: why droplets bead up, insects walk on water, and fluids climb narrow tubes against gravity.
6. Fluids in Motion: From Bernoulli to Turbulence
What changes when a fluid starts to flow. The continuity equation as mass conservation in steady flow. Bernoulli’s principle as energy conservation along a streamline. Viscosity and what it does to a real fluid in a pipe. The Reynolds number and the transition from smooth laminar flow to turbulence.
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 Bodies and Fluids 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.