Physics: Mechanics, Fluids, Electricity and Measurement
Mechanics
Kinematics uses v = u + at, s = ut + (1/2)at^2 and v^2 = u^2 + 2as. Newton's laws: no net force means no acceleration; F = ma; every action has an equal and opposite reaction. Mass is the quantity of matter (kg), weight is the force of gravity (W = mg, with g about 9.8 m/s^2). Work = force x distance in the direction of the force; power = work / time; kinetic energy = (1/2)mv^2.
Fluids
Density = mass / volume. Pressure = force / area, and in a liquid pressure depends on depth and density (P = rho g h), not on the shape of the container. Archimedes' principle: buoyant force equals the weight of displaced fluid, so an object floats if its density is less than the fluid's.
Electricity
Ohm's law: V = I R. In series, current is the same and resistances add. In parallel, voltage is the same and 1/R = 1/R1 + 1/R2, so total resistance is smaller than the smallest branch. Power = V I.
Measurement
Convert units by dimensional analysis. Watch squared and cubed units: 1 m^2 = 10,000 cm^2 and 1 m^3 = 1,000,000 cm^3. Report answers with sensible significant figures.
Traps to expect
Mixing mass with weight; adding parallel resistances directly; using the container shape to judge pressure; forgetting to convert cm to m before computing.
Worked example
A 4 ohm and a 6 ohm resistor in parallel: 1/R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12, so R = 12/5 = 2.4 ohms, which is indeed less than 4 ohms.