I'll create simple mini-games for every physics formula in the hub. Let me add a comprehensive game collection that covers all the formulas.

I've created a comprehensive physics game collection that covers every formula from the physics hub! Here's what I've built:

Complete Physics Game Collection

Game Categories:

Mechanics (4 games)

• Motion Calculator - v = d/t (velocity, distance, time)
• Force Calculator - F = ma (Newton's second law)
• Kinetic Energy - KE = ½mv² (moving objects)
• Potential Energy - PE = mgh (gravitational energy)

Electricity & Magnetism (3 games)

• Ohm's Law - V = IR (current, voltage, resistance)
• Electrical Power - P = VI (power calculations)
• Resistance Networks - Series/Parallel combinations

Waves & Sound (3 games)

• Wave Equation - v = fλ (wave speed)
• Pendulum Period - T = 2π√(L/g) (oscillations)
• Doppler Effect - f' = f(v±vᵣ)/(v±vₛ) (frequency shift)

️ Thermodynamics (3 games)

• Heat Transfer - Q = mcΔT (thermal energy)
• Ideal Gas Law - PV = nRT (gas properties)
• Temperature Conversion - °F, °C, K conversions

️ Modern Physics (3 games)

• Photon Energy - E = hf (quantum mechanics)
• Mass-Energy - E = mc² (Einstein's equation)
• Radioactive Decay - N = N₀e^(-λt) (nuclear physics)

Game Features:

Visual Elements:

• Animated backgrounds specific to each physics topic
• Moving cars for motion problems
• Sine waves for wave equations
• Circuit diagrams for electrical problems
• Swinging pendulums for oscillation problems
• Photon beams for quantum physics

Educational Design:

• Progressive difficulty - problems get harder with each level
• Real-world scenarios - practical physics applications
• Variable display - shows all given values clearly
• Formula reference - always visible for learning
• Instant feedback - immediate right/wrong responses

Game Mechanics:

• Scoring system - 50 points × level for correct answers
• Lives system - 3 lives, lose one for wrong answers
• Time limit - 3 minutes per game session
• Level progression - automatic advancement on correct answers
• Tolerance system - reasonable margin for error

Problem Types:

Each game generates random problems with:

• Varied scenarios (different contexts for same formula)
• Realistic values (appropriate ranges for each physics concept)
• Multiple unknowns (solve for different variables)
• Unit consistency (proper physics units throughout)

This creates a complete physics learning ecosystem where students can practice every major formula through engaging, interactive gameplay! 🚀

I'll fix the error by properly handling the variable names and ensuring all variables are correctly defined.

I've fixed the error by:

1. Properly defining the R variable in the gas-law case by explicitly setting R: R in the variables object
2. Using valid JavaScript property names - replaced special characters like ₀, ₛ, ₒ with regular characters (f0, vs, vo)
3. Replacing λ with wavelength and ΔT with deltaT to avoid Unicode issues
4. Ensuring all variables are properly declared before being used in the variables object

The error was occurring because JavaScript object property names with special Unicode characters (like subscripts and Greek letters) need to be handled differently, and some variables weren't properly defined before being referenced.

Now the game should work correctly without any reference errors! 🎮