Relates voltage (V), current (I), and resistance (R) for an ohmic conductor: V = I × R. Any two known values determine the third.
FORMULA
V = I R · I = V / R · R = V / IEXAMPLE
12 V across 4 Ω → I = 3 A. Electrical power P = V I = 36 W.
WHY IT MATTERS
Circuit debugging and resistor sizing start here. Non-ohmic devices need more care than a single R.
COMMON MISTAKES
- Mixing mA with A without converting
- Applying Ohm's law blindly to diodes, LEDs, or other non-ohmic parts
ELECTRICITY
Voltage (potential difference)
Electric potential difference between two points, measured in volts. It is the “push” that can drive current through a circuit.
EXAMPLE
A 9 V battery holds about 9 joules of potential energy difference per coulomb of charge between its terminals.
WHY IT MATTERS
Voltage without a closed path does not by itself guarantee current. Pair it with resistance and a circuit.
COMMON MISTAKES
- Treating voltage as synonymous with power or current
ELECTRICITY
Electric current
Flow of electric charge, measured in amperes (A). Conventional current direction is the flow of positive charge.
EXAMPLE
1 A means one coulomb of charge passing a point each second.
WHY IT MATTERS
Wire and fuse ratings care about current. Heat and voltage drop scale with I and I²R losses.
COMMON MISTAKES
- Reporting mA as A (off by 1000)
Opposition to current in a conductor, measured in ohms (Ω). For an ohmic device at fixed temperature, R = V / I.
EXAMPLE
If 5 V drives 0.01 A through a resistor, R = 500 Ω.
WHY IT MATTERS
Resistor choice sets current for a given voltage. Temperature and material change R in the real world.
COMMON MISTAKES
- Ignoring that resistance can change with temperature
Mass per unit volume: how much mass sits in a given space. Symbol ρ (rho). Units must match the reference table you compare to.
EXAMPLE
Mass 2 kg, volume 0.001 m³ → ρ = 2000 kg/m³. Pure water at standard conditions is about 1000 kg/m³.
WHY IT MATTERS
Buoyancy, material selection, and many fluid problems start with density.
COMMON MISTAKES
- Using g/cm³ and kg/m³ interchangeably without the ×1000 conversion
- Mixing mass and weight language when the lab asks for mass
MATTER & FLUIDS
Specific gravity
Ratio of a material's density to a reference density (often water at a stated temperature). Dimensionless; SG ≈ 1 means near water.
FORMULA
SG = ρ_material / ρ_referenceEXAMPLE
A liquid with density 800 kg/m³ vs water at 1000 kg/m³ has SG = 0.8.
WHY IT MATTERS
Industry datasheets often quote SG. Convert carefully before using SI density formulas.
COMMON MISTAKES
- Forgetting which reference fluid and temperature the SG table uses
Force per unit area acting perpendicular to a surface. SI unit is the pascal (Pa = N/m²). Gauge and absolute readings differ by atmospheric pressure.
EXAMPLE
Force 500 N on 0.25 m² → P = 2000 Pa (about 0.29 psi).
WHY IT MATTERS
Hydraulics, weather maps, and diving tables are pressure problems. Unit conversion is half the battle.
COMMON MISTAKES
- Mixing gauge and absolute pressure without saying which
- Using psi and Pa without converting
MATTER & FLUIDS
Gauge vs absolute pressure
Gauge pressure is relative to local atmosphere. Absolute pressure is relative to a perfect vacuum. Absolute ≈ gauge + atmospheric (about 101.3 kPa at sea level).
EXAMPLE
A tire at 220 kPa gauge is roughly 321 kPa absolute near sea level.
WHY IT MATTERS
Gas laws and many lab formulas want absolute pressure. Tire stickers usually quote gauge.
COMMON MISTAKES
- Feeding gauge pressure into an absolute-pressure formula
MOTION & FORCE
Speed & velocity
Speed is distance per time (a scalar). Velocity adds direction. Average speed = total distance ÷ elapsed time. Instantaneous speed needs a different model.
EXAMPLE
180 km in 2 h → average speed 90 km/h ≈ 25 m/s.
WHY IT MATTERS
Motion homework chains into acceleration and force. Unit mismatches (km/h vs m/s) cause silent errors.
COMMON MISTAKES
- Using km/h in formulas that expect m/s without converting
- Calling a trip average the same as instantaneous speed
MOTION & FORCE
Acceleration
Rate of change of velocity with time. Constant acceleration problems use kinematic equations; Newton's second law connects net force to acceleration.
FORMULA
a = Δv / Δt · F_net = m aEXAMPLE
0 to 20 m/s in 5 s → average a = 4 m/s². For 2 kg, F_net ≈ 8 N if that a is net.
WHY IT MATTERS
Braking distance, free fall, and dynamics labs all need a clear acceleration model.
COMMON MISTAKES
- Confusing acceleration with velocity
- Forgetting that direction changes also count as acceleration
MOTION & FORCE
Force (Newton's second law)
A push or pull that can change motion. Net force equals mass times acceleration when mass is constant: F_net = m a. Units: newtons (N).
EXAMPLE
10 kg at 2 m/s² → net force 20 N.
WHY IT MATTERS
Dynamics, friction, and inclined-plane problems start with identifying the net force, not any single force arrow.
COMMON MISTAKES
- Using weight (mg) as net force when other forces cancel or add
- Mixing grams and kilograms in F = ma
Energy transferred or converted per unit time. SI unit is the watt (W = J/s). Electrical power for DC ohmic circuits is often P = V I.
FORMULA
P = E / t · P = V I (DC ohmic)EXAMPLE
120 V and 2 A → 240 W. Run for 1 hour → energy 0.24 kWh.
WHY IT MATTERS
Motors, heaters, and electricity bills live in power and energy units.
COMMON MISTAKES
- Confusing watts (power) with kilowatt-hours (energy)
Energy of motion. Classical form is ½ m v² when speeds are far below the speed of light. Relativistic speeds need a different energy model.
FORMULA
KE = ½ m v² (classical)EXAMPLE
2 kg at 3 m/s → KE = 9 J.
WHY IT MATTERS
Collisions, braking, and many mechanics labs track kinetic energy alongside momentum.
COMMON MISTAKES
- Using classical KE near light speed
- Forgetting to use consistent SI units for m and v
An apparent-temperature index that combines air temperature and humidity to estimate how hot it feels. It is not the same number as a dry-bulb thermometer reading.
WHY IT MATTERS
Outdoor work and sports planning use heat index for heat-stress context. Recipes and lab work still need the thermometer reading.
COMMON MISTAKES
- Substituting heat index for air temperature in formulas that need dry-bulb T
An apparent-temperature index that combines air temperature and wind speed to estimate how cold exposed skin feels. It is not the air temperature itself.
WHY IT MATTERS
Cold-weather exposure planning uses wind chill. Equipment and chemistry still care about actual air temperature.
COMMON MISTAKES
- Using wind chill as the oven or lab ambient temperature
ASTROPHYSICS
Black hole collision (GW sketch)
When two black holes merge, the remnant mass is less than the sum of the parents because energy radiates in gravitational waves. Educational calculators sketch chirp mass and radiated energy with strong model limits.
WHY IT MATTERS
Builds intuition for LIGO/Virgo headlines. Not a research-grade waveform or personal physics engine.
COMMON MISTAKES
- Treating a teaching sketch as a published GW event analysis
- Using non-relativistic kinetic energy near c