Mass

Mass ($m$) measures an object’s inertia: how strongly it resists changes in motion. More mass means the same applied net force produces less acceleration:

$${\vec{F}}_{net}=m\vec{a}$$

Mass is not the same as weight. Mass is intrinsic to the object; weight is the gravitational force on that mass. Near Earth’s surface,

$$W=mg$$

where $g\approx 9.81\mathrm{m}{\mathrm{s}}^{-2}$.

Why it matters

• In Newton’s Laws of Motion, mass links force and acceleration.
• In Momentum, mass scales the quantity of motion: $\vec{p}=m\vec{v}$.
• In kinetic Energy, mass appears as $K=\frac{1}{2}m{v}^2$.

Mass is believed to arise through interactions with fields including the Higgs field, but in classical mechanics we usually treat it as a given property.

Unit: Kilogram.

Common checks

Do not confuse mass with volume or density. A small dense object can have more mass than a large low-density one. Also, mass is a scalar: it has size but no direction. In most introductory mechanics problems, mass is constant, which is why $\vec{F}=m\vec{a}$ and $\vec{p}=m\vec{v}$ are safe shortcuts.