Physics Equation Studio
The language of the universe expressed in math. Reference, Solve, and Memorize key physics laws.
| Equation Name | Formula | Variables | Field |
|---|---|---|---|
Newton's Second Law | F = ma | F: Force, m: Mass, a: Acceleration | Mechanics |
Kinetic Energy | KE = ½mv² | m: Mass, v: Velocity | Energy |
Gravitational Potential Energy | PE = mgh | m: Mass, g: Gravity, h: Height | Energy |
Ohm's Law | V = IR | V: Voltage, I: Current, R: Resistance | Electricity |
Hooke's Law | F = -kx | F: Force, k: Spring constant, x: Extension | Mechanics |
Density | ρ = m/V | ρ: Density, m: Mass, V: Volume | Fluid Mechanics |
Pressure | P = F/A | P: Pressure, F: Force, A: Area | Fluid Mechanics |
Wave Speed | v = fλ | v: Speed, f: Frequency, λ: Wavelength | Waves |
Power | P = W/t | P: Power, W: Work, t: Time | Energy |
Momentum | p = mv | p: Momentum, m: Mass, v: Velocity | Mechanics |
Ideal Gas Law | PV = nRT | P: Pressure, V: Volume, n: Moles, R: Gas Constant, T: Temp | Thermodynamics |
Einstein's Energy | E = mc² | E: Energy, m: Mass, c: Speed of Light | Relativity |
Snell's Law | n₁sin(θ₁) = n₂sin(θ₂) | n: Refractive Index, θ: Angle | Optics |
Coulomb's Law | F = k(q₁q₂)/r² | F: Force, q: Charge, r: Distance | Electricity |
Frequency & Period | f = 1/T | f: Frequency, T: Period | Waves |
Work (Calculus) | W = ∫ F dx | W: Work, F: Force, x: Displacement | Mechanics |
Sum of Forces | ΣF = ma | Σ: Summation, F: Force, m: Mass | Mechanics |
Change in Velocity | a = ∆v/∆t | a: Accel, ∆v: Change in vel | Kinematics |
Electric Field (Potential) | E = -∇V | E: Field, ∇: Gradient, V: Potential | Electromagnetism |
Product Notation | P = ∏ x_i | ∏: Product, x: Terms | Math |
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Unlocking the Universe with Math
Physics is not just about memorizing formulas; it's about understanding the relationships they represent. An equation is a sentence. F = ma isn't just letters; it says "The push you need (Force) depends on how heavy the object is (Mass) and how fast you want to speed it up (Acceleration)."
Core Pillars of Physics
Most introductory physics courses revolve around three main pillars:
Mechanics
The study of motion.
- • F=ma: Newton's 2nd Law
- • p=mv: Momentum
- • W=mg: Weight
Electricity
The flow of charge.
- • V=IR: Ohm's Law
- • P=IV: Electric Power
- • F=kqq/r²: Coulomb's Law
Energy
The potential to do work.
- • KE=½mv²: Kinetic Energy
- • PE=mgh: Potential Energy
- • E=mc²: Mass-Energy
How to Use the Solvers
We've built interactive calculators for the most common equations. Simply switch to the "Interactive Solvers" tab. Instead of manually punching numbers into a calculator, you can tweak the Inputs (like Mass or Voltage) and instantly see how the Output (Force or Current) changes. This is a great way to develop an intuition for proportionality.
Study Tips
- Dimensional Analysis: Always check your units. If you are solving for Force, your answer must be in Newtons (kg·m/s²). If your math gives you kg/s, you made a mistake.
- Limits: Test extreme cases. What happens if Mass is zero? What happens if Radius is infinite? The equation should behave logically.
- Use the Flashcards: The "Study Flashcards" tab is designed to help you memorize these formulas for exams. Try to say the formula out loud before flipping the card!
Frequently Asked Questions
Why is F=ma so important?
Newton's Second Law (F=ma) is the bridge between force and motion. It tells us that an object will only accelerate if a net force acts on it, and the acceleration is proportional to that force. It is the foundation of classical mechanics.
What is the difference between Speed and Velocity?
Speed is a scalar quantity (just magnitude, e.g., 50 mph). Velocity is a vector quantity (magnitude + direction, e.g., 50 mph North). In equations, 'v' usually stands for velocity, but in 'KE = ½mv²', direction doesn't matter, so it acts like speed.
How do I solve for 'm' in F=ma?
Algebraically rearrange the formula. If F = ma, divide both sides by 'a'. This gives you m = F/a. Our interactive solver does this for you automatically!
When does Ohm's Law (V=IR) not apply?
Ohm's Law only applies to 'Ohmic' materials (like standard resistors and wires) where resistance is constant. It breaks down for components like diodes, transistors, or light bulbs where resistance changes with temperature or voltage.
Why is energy squared in E=mc²?
The 'c²' is the conversion factor between mass and energy. Because the speed of light (c) is a huge number (3x10^8 m/s), squaring it produces an enormous number. This explains why a tiny amount of mass (like in a nuclear reaction) can release a massive amount of energy.
What is the 'μ' symbol in friction formulas?
The symbol 'μ' (mu) represents the Coefficient of Friction, a unitless number that describes how 'grippy' two surfaces are. A high μ (like rubber on concrete) means high friction; a low μ (like ice on steel) means low friction.
Does gravity 'g' always equal 9.8 m/s²?
Only near the surface of Earth! On the Moon, g is about 1.6 m/s². Even on Earth, it varies slightly—it's stronger at the poles and weaker at the equator due to Earth's rotation and shape.