The key difference between gravitational mass and inertial mass is that gravitational mass is measured under gravity, whereas inertial mass is measured under any force.
Mass is a property of a substance as well as its resistance towards acceleration. There are two types of mass as gravitational mass and inertial mass, which give the type of force acting on the mass. Gravitational force is the reason for acceleration due to gravity, and we can measure the mass of an object that moves due to gravity.
CONTENTS
1. Overview and Key Difference
2. What is Gravitational Mass
3. What is Inertial Mass
4. Side by Side Comparison – Gravitational Mass vs Inertial Mass in Tabular Form
5. Summary
What is Gravitational Mass?
Gravitational mass is the mass that an object has due to gravitational force. We can determine it by the strength of the gravitational force experienced by an object. Here, the object should be in a gravitational field, denoted by “g”. Typically, we measure this mass in comparison with the mass (due to gravity) of a known object. We can do this with a balance scale.
According to Newton’s law of universal gravitation, there is a gravitational force between any pair of objects. For the calculation of gravitational mass, we can use the following equation;
F = Gm1m2/r2
Where F is the applied force, G is gravitational constant, m1 and m2 are the gravitational masses of each object and r is the distance between them.
Figure 01: Two Objects at Gravitational Force in a Diagram
There are two types as active and passive gravitational mass; active form is a measure of mass due to gravitational flux (measured by allowing a small object to fall freely under gravity). The passive form is a measure of the strength of the object’s interaction with a gravitational field (measured by dividing an object’s weight by its free-fall acceleration).
What is Inertial Mass?
Inertial mass is the resistance to acceleration due to any force, and we can obtain it by applying a force which causes an acceleration of that mass. If this force is a gravitational force, we can call it “gravitational mass”, but if it is a different force, we call it “inertial mass” as a general term. In order to determine the inertial mass, we can apply Newton’s law;
F = ma
m = F/a
Where F is the force that acts on the mass, a is the acceleration due to the force and m is the mass of the object.
What is the Difference Between Gravitational Mass and Inertial Mass?
Gravitational mass and inertial mass are two types of masses. The key difference between gravitational mass and inertial mass is that gravitational mass is measured under gravity, whereas inertial mass is measured under any force. When taking the measurement, we can take the measurement for gravitational mass by allowing a test object to fall freely under gravity. We can measure inertial mass by applying a force to give an acceleration on an object. Moreover, we can use Newton’s law of universal gravity to calculate gravitational mass and Newton’s second law to calculate inertial mass. This is another difference between gravitational mass and inertial mass.
Summary – Gravitational Mass vs Inertial Mass
Gravitational mass and inertial mass are two forms of masses. The key difference between gravitational mass and inertial mass is that gravitational mass is measured under gravity, whereas inertial mass is measured under any force.
Reference:
1. Faller, James E., and Alan H. Cook. “Gravity.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 10 Apr. 2019, Available here.
Image Courtesy:
1. “NewtonsLawOfUniversalGravitation” By I, Dennis Nilsson (CC BY 3.0) via Commons Wikimedia