Physics Through Energy and Equilibrium
Move beyond tedious force calculations by learning how physicists actually analyze motion. Discover how energy landscapes, reference frames, rotational inertia, and resonance reveal how physical systems settle, collide, and spin.
Like Duolingo, but for Physics Through Energy and Equilibrium. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
A short one: 12 levels across 2 sections, about 24 minutes end to end, roughly 5 days at five minutes a day. It moves through Predicting Motion with Invariants and Governing Rotations and Oscillations. It assumes you already know the basics.
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Key ideas in Physics Through Energy and Equilibrium
- Kinetic energy cannot be negative, so potential energy cannot exceed total energy.
- Total mechanical energy forms a strict ceiling on the potential energy curve.
- Regions where the curve rises above the total energy line are physically forbidden.
- At the intersection of total energy and potential energy, kinetic energy is zero.
- A zero-velocity point with non-zero slope reverses the particle's direction.
- These intersection boundaries bound the allowable motion without solving velocities.
- A local minimum in potential energy forms a stable equilibrium well.
- Nudging an object up either side produces a restoring force back to the center.
- The force always acts opposite to displacement inside a potential energy well.
- Local peaks represent unstable equilibrium where slope is zero at the very top.
- Displacing an object off a peak creates a force pointing down and away from it.
- Flat plateaus produce neutral equilibrium with zero net force rather than runaway.
- Force is the negative slope of the potential energy curve.
- Steeper slopes generate stronger forces, while flat regions exert zero force.
- The force vector always points downhill toward lower potential energy.
- In the center-of-mass frame, the system's total net momentum is always zero by definition.
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives Physics Through Energy and Equilibrium the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
When you draw an energy graph, what role does the total mechanical energy line play?
Get it right to open this lesson and 11 more in the app.
Where Physics Through Energy and Equilibrium takes you
- 1
Predicting Motion with Invariants
- Reading Potential Energy Landscapes
- Simplifying Collisions with Moving Frames
- 2
Governing Rotations and Oscillations
- Predicting Rotational Motion and Precession
- Tuning Oscillations and Managing Resonance
2 sections · 4 units · 12 levels. Built to play, not to enroll.
Tomo is in ChatGPT
Tomo is also a ChatGPT plugin: the same playable courses, built and played inside your chat.
Add Tomo to ChatGPT- What to ask
- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
- What you get
- Quick questions with instant feedback, hearts and stars, ready to play in about a minute.
- Where it goes
- No sign-up to start. Connect your Tomo account and your streak carries on in the app.
You pick the voice
Physics Through Energy and Equilibrium is taught in the Bestie style: your friend who just gets it. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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Start Physics Through Energy and Equilibrium today.
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