Mechanics of Bodies and Fluids
Real mechanics of bodies and fluids for talented high schoolers.
Online from anywhere · or in-person in Princeton, NJ
A World Through the Lens of Mechanics of Bodies and Fluids
Mechanics of Bodies and Fluids is one of the six classical core courses of the Physics Lyceum: High School curriculum, taught on the Deep Physics model that runs through the whole SoTS Physics Lyceum.
The course runs on theory, problem-solving sessions, homework, and practical laboratory work. The Lyceum provides the equipment, and tuition covers it.
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, worked up to the precession of the equinoxes, the slow wheel of the Earth’s own axis.
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.