Absolute Acceleration

Absolute acceleration is the measurement of the total acceleration experienced by an object, including the component due to Earth’s gravity g, as detected directly by an accelerometer.

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How to measure it in class

With the FizziQ app, it is easy to measure the absolute acceleration of the smartphone and to compare it with the value of g.

Steps:

Open FizziQ and select the absolute acceleration sensor (acceleration with g). Place the smartphone flat on the table and note the displayed value: it should be close to 9.81 m/s².
Gradually tilt the smartphone and observe how the components of the absolute acceleration are distributed over the three axes x, y and z. Verify that the magnitude remains constant and equal to g.
Drop the smartphone from a few centimeters above a cushion (carefully) and observe the fall in the data. During free fall, the absolute acceleration drops toward zero.
Compare the results with FizziQ’s linear acceleration sensor (without g). Discuss: why do the two sensors give different results for a stationary object?

Scientific activities on this topic

Several experiments easily performed with a smartphone, a tablet or a computer allow you to measure and understand absolute acceleration.

Learn more

Einstein’s equivalence principle

In 1907, Albert Einstein had what he called “the happiest thought of his life”. He realized that an observer in free fall feels no gravity: their accelerometer reads zero. Conversely, an accelerated observer in space feels exactly the same effects as gravity. This equivalence between acceleration and gravity became the foundation of general relativity.

MEMS accelerometers and the measurement of absolute acceleration

Smartphone accelerometers are MEMS devices (Micro-Electro-Mechanical Systems) a few millimeters across. They contain a micro-mass suspended by microscopic springs. When the smartphone accelerates, the mass moves relative to the casing. This displacement is measured through a change in electrical capacitance. The sensor naturally measures absolute acceleration, and it is software processing that subtracts g to obtain the linear acceleration.

Applications in inertial navigation

Inertial navigation systems use accelerometers and gyroscopes to determine the position of a vehicle without GPS. Submarines, airplanes and rockets carry inertial units that integrate the absolute acceleration twice to obtain the position. The required precision is extreme: an error of 0.001 m/s² translates, through the relation d = ½at², into a drift of about 6.5 km after one hour of navigation.

Orders of magnitude

Absolute acceleration at rest: 9.81 m/s². In free fall: 0 m/s². In an elevator going up: about 10.5 m/s². In an airplane at takeoff: about 12 to 14 m/s². In a training centrifuge for pilots: up to 90 m/s² (about 9 g). On the Moon at rest: 1.62 m/s².

Formula

Absolute acceleration is expressed as the sum of the motion acceleration and the gravitational acceleration:

a_absolute = a_motion + g

Meaning: a_absolute: total acceleration measured by the sensor (m/s²) a_motion: acceleration related to the object’s own motion (m/s²) g: gravitational acceleration, approximately 9.81 m/s² directed downward

The magnitude of the absolute acceleration at rest is: |a_absolute| = g ≈ 9.81 m/s²

Application examples

A smartphone placed on a table displays an absolute acceleration of 9.81 m/s² upward
In free fall, a skydiver measures an absolute acceleration close to zero before the parachute opens
A passenger in an airplane in level flight measures an absolute acceleration equal to g, just like on the ground
In an elevator accelerating upward, the absolute acceleration exceeds 9.81 m/s²
An astronaut in weightlessness in the ISS measures an absolute acceleration close to zero

FAQ

Q: Why does a stationary object measure an acceleration of 9.81 m/s²? A: The accelerometer detects the reaction force exerted by the surface on which it rests. This force, equal and opposite to the weight, is interpreted as an upward acceleration of value g.

Q: What is the difference between absolute acceleration and linear acceleration? A: Absolute acceleration includes the gravitational component g. Linear acceleration is corrected: the software subtracts g to keep only the acceleration related to motion.

Q: Does absolute acceleration change with altitude? A: Yes, very slightly. The value of g decreases with altitude, but the variation is too small to be detected by a smartphone under ordinary classroom conditions.

Q: Can g be measured with absolute acceleration? A: Yes. By placing the smartphone motionless on a horizontal surface, the measured absolute acceleration corresponds directly to the local value of g.

Q: Why is absolute acceleration zero in free fall? A: In free fall, the smartphone and its sensor fall together. No contact force acts on the sensor’s test mass, which therefore measures zero.

Linear Acceleration - Accelerometer - Gravitational Acceleration - Free Fall