Motion, Forces and Energy - Mass, weight and density

Mass ($m$) is a measure of the quantity of matter in an object at rest relative to the observer. It is measured in kilograms ($kg$) and remains constant regardless of location.

Weight ($W$) is the gravitational force acting on an object that has mass. It is measured in Newtons ($N$) and changes depending on the gravitational field strength ($g$).

The gravitational field strength ($g$) is the force per unit mass, expressed as $g = \frac{W}{m}$. On Earth, $g$ is approximately $9.8 \text{ N/kg}$ (or $10 \text{ N/kg}$ for some IGCSE syllabus variations).

Density ($\rho$) is defined as the mass per unit volume of a substance. The standard SI unit is $kg/m^3$, but $g/cm^3$ is frequently used in laboratory experiments ($1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3$).

To determine the density of an irregularly shaped solid, the displacement method is used: the volume of the solid is equal to the volume of liquid it displaces in a measuring cylinder.

Objects float in a fluid if their density is less than the density of the fluid ($\rho_{object} < \rho_{fluid}$) and sink if their density is greater.