What is the Difference Between Gravitational Mass and Inertial Mass?

The main difference between gravitational mass and inertial mass lies in their definitions and how they are measured, although their values are identical. Here are the key differences:

Inertial Mass: This is defined by Newton's second law, $$F = ma$$, which states that when a force is applied to an object, it will accelerate proportionally, and the constant of proportion is the mass of that object. Inertial mass is measured by applying a force to an object and observing its acceleration.
Gravitational Mass: This is described by the force of gravity on an object in a gravitational field. Gravitational mass is typically measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass, often using a balance scale.

The fact that gravitational mass and inertial mass have the same value is known as the "equivalence of mass". This equivalence is a fundamental principle in physics and is the basis for Einstein's Theory of General Relativity. The equivalence of these two masses is also why all objects fall at the same rate on Earth.

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What is the Difference Between Gravitational Mass and Inertial Mass?

Comparative Table: Gravitational Mass vs Inertial Mass

The main difference between gravitational mass and inertial mass lies in the forces they are associated with and the methods used to measure them. Here is a table summarizing the differences:

Property	Gravitational Mass	Inertial Mass
Definition	Gravitational mass is a measure of the strength of the gravitational force acting on an object.	Inertial mass is a measure of an object's resistance to changes in its motion.
Measurement Method	Gravitational mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass, typically using a balance scale.	Inertial mass is measured by applying a force to give an acceleration on an object and using Newton's second law (F = ma) to calculate the mass.
Formula	gravitational mass: $$m = \frac{F{grav}}{g}$$, where $$F{grav}$$ is the gravitational force and g is the acceleration due to gravity.	inertial mass: $$m = \frac{F}{a}$$, where F is the force that acts on the mass and a is the acceleration due to the force.
Equivalence	As far as we can measure, gravitational mass and inertial mass are equal for all objects.	The equivalence of gravitational and inertial mass is why all objects fall at the same rate on Earth.

The equality of gravitational and inertial mass is a fundamental principle in physics and is one of the key principles that led to the development of Einstein's General Relativity.

Guilherme Mazui

Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.