Which calculator for which situation
- Motion. Speed, distance and time for the uniform case; average speed when a journey has different legs; acceleration for change in velocity; free fall for motion under gravity alone.
- Energy and force. Kinetic energy and potential energy; force by Newton's second law; work and power for the energetic cost of an action.
- Electricity. Ohm's law relates voltage, current and resistance; equivalent resistance solves series and parallel networks.
- Matter. Density, the ratio of mass to volume that explains what floats and what sinks.
The two things intuition gets wrong in physics
1. Velocity is squared. Kinetic energy is m·v²/2. Doubling speed does not double energy — it quadruples it. A car at 60 mph carries four times the energy of the same car at 30, and that energy is what the structure has to absorb in a collision. The same relationship is why braking distance grows with the square of speed.
2. Mass cancels in free fall. A hammer and a feather fall together in a vacuum. Gravity's pull is proportional to mass, but inertia — the resistance to being accelerated — is proportional to mass too. The two cancel, leaving the same acceleration for every body. In air, what separates them is not gravity but air resistance, which weighs proportionally more on the lighter object.
Units: where calculations break
Physics is the field where a wrong unit does not produce a strange result — it produces a plausible, wrong one. Three habits catch nearly all of it:
- Convert speed before using it. The formulas work in m/s. From mph, multiply by 0.447.
- Use kilograms, not grams. A joule is kg·m²/s². Mass in grams gives a result a thousand times too small with no warning.
- Check the unit of the answer. Energy in joules, force in newtons, power in watts. If your calculation returns something else, the formula is incomplete.
Frequently asked questions
Why is g 9.8 and not 10? 9.8 m/s² is the average at Earth's surface; the real value runs from about 9.78 at the equator to 9.83 at the poles, because of the planet's oblateness and rotation. Using 10 simplifies the arithmetic with a 2% error.
Do the formulas account for friction and air resistance? No. These are the idealised models taught in introductory physics, and they describe dense objects over short distances well. For a sheet of paper, a skydiver or a car at highway speed, air resistance dominates and the model stops applying.
What is the difference between mass and weight? Mass is the quantity of matter, in kilograms, and does not change from place to place. Weight is the force gravity exerts on that mass, in newtons — on the Moon your mass is identical and your weight is one sixth.
Are energy and power the same? No. Energy is the amount of work; power is how fast it is done. Climbing stairs running or walking costs the same energy — running demands more power.