Deep Physics: Mechanics of Bodies and Fluids for Talented High Schoolers, Princeton
Real mechanics for things that spin, balance, and flow. Rotational dynamics, statics, and hydrostatics, taught from first principles. For talented high schoolers.
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.
This course teaches you what physicists actually know about it. From first principles.
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.
By the end, you will think about rotation, balance, and flow the way a physicist thinks about them.
What You Will Actually Understand
By the end of the course, you will understand six core ideas of the mechanics of bodies and fluids.
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.
3. Static Equilibrium
When forces and torques both add to zero. The two conditions for static equilibrium. Center of mass and center of gravity. Stability of structures. Worked problems on bridges, beams, and ladders.
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
Why a boat floats and a fish is not crushed at depth. Pressure, density, and the hydrostatic pressure equation. Pascal’s principle. Buoyancy and Archimedes’ principle. Surface tension at the level needed to set up problems.
6. Fluids in Motion
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. Applications from a pipe with a constriction to lift on a wing, with the limits of the model marked.
The specific topics, and the depth given to each, may shift depending on class priorities and the dynamics of the cohort. The destination, a working understanding of rotational mechanics and the mechanics of fluids, stays the same.
Schedule, Pricing & Enrollment
Formats: Fall, Spring, and Summer semesters.
Schedule, format, tuition, refund policy, and transcripts 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 eight semester-long physics courses in the SoTS Physics Lyceum: a multi-year curriculum in Princeton, NJ.
Mechanics of motion. Mechanics of bodies and fluids. Waves and oscillations. Thermodynamics. Electricity and magnetism. Optics and atomic structure. Special Relativity. Quantum mechanics.
The Lyceum is built on the Deep Physics methodology.