Inertial vs Gravitational Mass (College Board AP® Physics 1: Algebra-Based)
Study Guide
Written by: Ann Howell
Reviewed by: Caroline Carroll
Inertial versus gravitational mass
Inertial mass
Objects have inertial mass, or inertia
Inertia is a property that determines how much an object’s motion resists changes when interacting with another object
Newton's second law is used to calculate inertial mass
Measuring inertial mass
The inertial mass of an object can be determined by applying a force to accelerate the mass
This is commonly done by setting a mass oscillating on the end of a spring with a spring constant, , and calculating the time period
Measuring inertial mass using a mass-spring system
Set the mass oscillating and record the time for 10 oscillations using a stop watch
One oscillation involves the mass moving up to the top and back down to the bottom
Divide the total time for the 10 oscillations by 10 to obtain the time period
The time period is the time for one oscillation
Using the equations for centripetal force, angular velocity and time period an equation for the spring constant, , and the time period is obtained to calculate the inertial mass of the object
Gravitational mass
Gravitational mass is related to the force of attraction between two systems with mass
Newton's law of gravitation is used to calculate the gravitational mass
Measuring gravitational mass
The gravitational mass of an object can be determined by placing the object in a gravitational field and measuring the gravitational force, , on the mass
This is commonly done by balancing the mass on a set of balance scales
The magnitude of the masses needed for the scales to be balanced (sitting horizontally on the pivot) is equal to the gravitational mass of the object
The balance scales below sit horizontally, showing that four single masses on the right equal the gravitational mass of the object on the left
Measuring gravitational mass using a balance scale
Equivalence principle
Inertial mass and gravitational mass have been experimentally verified to be equivalent
Using the experimental methods above, the inertial and gravitational masses of an object are found to be the same
Algebraically, this means
So, when
Then the object accelerates at the same rate as the magnitude of the gravitational field strength
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