 Mass

Mass measures a body's resistance to a change of velocity and its coupling to gravity. In Newton's second law for a body of fixed mass, $\mathbf{F}=m\mathbf{a}$, the inertial mass relates a known net force to the resulting acceleration. Applying the same force to two carts and comparing their accelerations measures their mass ratio.

A balance instead compares gravitational forces in a common gravitational field, probing gravitational mass. The proportionality of inertial mass and gravitational mass explains why freely falling bodies have the same acceleration when other forces can be neglected. Gravitational weight changes with the local gravitational field, while a body's mass need not change. In special relativity, mass-energy equivalence relates rest energy to mass through $E_0=m{c}^2$.

Mass is a measure of the amount of matter in an object or substance. It is a fundamental property in physics and is typically measured in units such as grams (g) or kilograms (kg). Mass is a scalar quantity, meaning it has magnitude but no direction.