Resource Lesson
Inertial vs Gravitational Mass
Printer Friendly Version
Usually when we speak of an object's mass we do not distinguish whether we are referring to its inertial mass or its gravitational mass. This is because the quantity of matter present in an object, i.e., its mass, does not depend on the method by which it is measured.
Gravitational mass
is measured with the use of a double-pan or triple-beam balance. It is a
static measurement
- that is, a measurement that can only be accurately recorded when the system is in a state of rest. This method involves placing an unknown mass on the pan and using countermasses to return the balance to equilibrium.
This type of measurement only works in the presence of gravity and is actually based on the torque produced by the product of the weights and their lever-arms' distance from the axis of rotation. Since torques produce rotation, when the clockwise torque caused by the countermasses equals the counterclockwise torque caused by the unknown mass, we say that the balance is in equilibrium. Since the balance will then be in a state of rest, we can read the correct value for the unknown's gravitational mass from the balance's scale.
Inertial mass
is measured with the use of an inertial balance, or spring-loaded pan. It is a
dynamic measurement
- that is, a measurement that can only be accurately recorded while the system is in a state of motion. This method capitalizes on an object's inertia, or its tendency to continue in its current state of motion, as a means of quantifying the amount of matter present.
The pan is first calibrated by counting the number of vibrations in a specified amount of time produced by two objects whose masses are known. From this information, the
period
(represented with the variable
T
) of each object's mass is calculated by dividing the total amount of time by the total number of vibrations. Period is usually measured in terms of seconds per vibration. These two periods are then plotted on a graph of T
^{2}
vs Mass.
Subsequent knowledge of the vibrational period of any unknown mass will allow its inertial mass to be interpolated from this calibration graph. This type of balance will measure an object's inertial mass even in the absence of gravity.
A dramatic use of these two definitions of mass can be illustrated when we state that all
freely falling bodies
experience the same acceleration. When you use
net F = ma
for a projectile in freefall,
net F
equals the force of gravitational attraction between the object and the Earth; that is, the object's weight. Weight is calculated as the product of the object's gravitational mass and the Earth's gravitational field strength,
g
.
wt = mg
When we look at the other side of the equation,
ma
, then we are talking about the object's inertial mass - its resistance to a change in its state of motion, that is, its resistance to being accelerated. This mass is a measure of how much inertia must be accelerated.
net F = ma
-m
_{gravitational}
g = m
_{inertial}
a
Since we can experimentally determine that all freely-falling bodies experience the same acceleration, that is, a = -g, we have proof that
m
_{gravitational}
= m
_{inertial}
and there is no need to distinguish between the two definitions.
The value of an object's mass is unique, independent of its method of measurement.
Related Documents
Lab:
Labs -
Coefficient of Friction
Labs -
Coefficient of Friction
Labs -
Conservation of Momentum in Two-Dimensions
Labs -
Falling Coffee Filters
Labs -
Inelastic Collision - Velocity of a Softball
Labs -
Inertial Mass
Labs -
LabPro: Newton's 2nd Law
Labs -
Loop-the-Loop
Labs -
Mass of a Rolling Cart
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Relationship Between Tension in a String and Wave Speed
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
Labs -
Static Equilibrium Lab
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: LabPro Data for Hooke's Law
Labs -
Terminal Velocity
Labs -
Video LAB: A Gravitron
Labs -
Video LAB: Ball Re-Bounding From a Wall
Resource Lesson:
RL -
Advanced Gravitational Forces
RL -
Air Resistance
RL -
Air Resistance: Terminal Velocity
RL -
Forces Acting at an Angle
RL -
Freebody Diagrams
RL -
Gravitational Energy Wells
RL -
Inclined Planes
RL -
Newton's Laws of Motion
RL -
Non-constant Resistance Forces
RL -
Properties of Friction
RL -
Springs and Blocks
RL -
Springs: Hooke's Law
RL -
Static Equilibrium
RL -
Systems of Bodies
RL -
Tension Cases: Four Special Situations
RL -
The Law of Universal Gravitation
RL -
Universal Gravitation and Satellites
RL -
Universal Gravitation and Weight
RL -
Welcome! What is Mass?
RL -
Work and Energy
Worksheet:
APP -
Big Fist
APP -
Family Reunion
APP -
The Antelope
APP -
The Box Seat
APP -
The Jogger
CP -
Action-Reaction #1
CP -
Action-Reaction #2
CP -
Equilibrium on an Inclined Plane
CP -
Falling and Air Resistance
CP -
Force and Acceleration
CP -
Force and Weight
CP -
Force Vectors and the Parallelogram Rule
CP -
Freebody Diagrams
CP -
Gravitational Interactions
CP -
Incline Places: Force Vector Resultants
CP -
Incline Planes - Force Vector Components
CP -
Inertia
CP -
Mobiles: Rotational Equilibrium
CP -
Net Force
CP -
Newton's Law of Motion: Friction
CP -
Static Equilibrium
CP -
Tensions and Equilibrium
NT -
Acceleration
NT -
Air Resistance #1
NT -
An Apple on a Table
NT -
Apex #1
NT -
Apex #2
NT -
Falling Rock
NT -
Falling Spheres
NT -
Friction
NT -
Frictionless Pulley
NT -
Gravitation #1
NT -
Head-on Collisions #1
NT -
Head-on Collisions #2
NT -
Ice Boat
NT -
Rotating Disk
NT -
Sailboats #1
NT -
Sailboats #2
NT -
Scale Reading
NT -
Settling
NT -
Skidding Distances
NT -
Spiral Tube
NT -
Tensile Strength
NT -
Terminal Velocity
NT -
Tug of War #1
NT -
Tug of War #2
NT -
Two-block Systems
WS -
Advanced Properties of Freely Falling Bodies #1
WS -
Advanced Properties of Freely Falling Bodies #2
WS -
Calculating Force Components
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Combining Kinematics and Dynamics
WS -
Distinguishing 2nd and 3rd Law Forces
WS -
Force vs Displacement Graphs
WS -
Freebody Diagrams #1
WS -
Freebody Diagrams #2
WS -
Freebody Diagrams #3
WS -
Freebody Diagrams #4
WS -
Introduction to Springs
WS -
Kinematics Along With Work/Energy
WS -
Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
net F = ma
WS -
Practice: Vertical Circular Motion
WS -
Ropes and Pulleys in Static Equilibrium
WS -
Standard Model: Particles and Forces
WS -
Static Springs: The Basics
WS -
Vocabulary for Newton's Laws
WS -
Work and Energy Practice: Forces at Angles
TB -
Systems of Bodies (including pulleys)
TB -
Work, Power, Kinetic Energy
PhysicsLAB
Copyright © 1997-2016
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton